(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 12.3' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 126557, 3239] NotebookOptionsPosition[ 118868, 3107] NotebookOutlinePosition[ 119303, 3124] CellTagsIndexPosition[ 119260, 3121] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Get", "[", "\"\\"", "]"}]], "Input", CellChangeTimes->{{3.832151022612398*^9, 3.832151030465872*^9}, { 3.8321511379667025`*^9, 3.8321511785398226`*^9}, 3.832151627377406*^9}, CellLabel->"In[5]:=",ExpressionUUID->"aff1ddef-8716-4588-a33d-a6327039d59d"], Cell[CellGroupData[{ Cell[BoxData[ InterpretationBox[ RowBox[{"\<\"The currently installed versions of IGraph/M are: \"\>", "\[InvisibleSpace]", RowBox[{"{", "}"}]}], SequenceForm["The currently installed versions of IGraph/M are: ", {}], Editable->False]], "Print", CellChangeTimes->{3.8321516294929905`*^9}, CellLabel-> "During evaluation of \ In[5]:=",ExpressionUUID->"6bc201f1-e6df-4076-bf01-856fe692e727"], Cell[BoxData[ InterpretationBox[ RowBox[{"\<\"Installing IGraph/M is complete: \"\>", "\[InvisibleSpace]", InterpretationBox[ RowBox[{ TagBox["PacletObject", "SummaryHead"], "[", DynamicModuleBox[{Typeset`open$$ = False, Typeset`embedState$$ = "Ready"}, TemplateBox[{ PaneSelectorBox[{False -> GridBox[{{ PaneBox[ ButtonBox[ DynamicBox[ FEPrivate`FrontEndResource["FEBitmaps", "SummaryBoxOpener"], ImageSizeCache -> { 7.0230560307297845`, {0., 7.0230560307297845`}}], Appearance -> None, BaseStyle -> {}, ButtonFunction :> (Typeset`open$$ = True), Evaluator -> Automatic, Method -> "Preemptive"], Alignment -> {Center, Center}, ImageSize -> Dynamic[{ Automatic, 3.5 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[ Magnification])}]], GraphicsBox[ TagBox[ RasterBox[CompressedData[" 1:eJzFmAdQG1cax5m7ubnMzZXM+O4myTnJ2U4mmUm55HJOgn2xg00cF+KCu42x g2OwMW6iRQZswKaEGmODwPReDKJJdCEQRTQZjEAIiSoJ1ECoSyut9rulnCtu TLj7j7Qjrd5732//33v7vtUqpwv2zr+ysrJyfwU/2H/vbUMgfE/c+yr+Zf95 9zMu50/9sO28xymXU4QvnX6Nn/x44T37Gf4roVDIYDAoc6Ius+aj1NfX83g8 eFQ1NTUBAQHu7u7+/v6BgYEBy6zAOXl5efn4+BQUFOh0uvsYBAIhLi6OxWKN jY0JBIKxl9H4nF62Cx6FzWZnZmZ6eHjgR7PZPDIycvny5YSEBKVSCf9zoSia n5+P56Kjo6OsrMzb23toaGjJo5nMJq1Ws+TuuANhYWGJiYnJyckxMTF6vX5p 48hEoxvWr1u1ek33vbtLhsFtmYchkUgGg2EpQ6g5t4NcrebkRNhlBMGSSSIj I3FPYmNj78/el1D3bVHR+cCK6o32pzau3ZX2U24FJ4hjLlgCSW5ublRU1BJI MJ0Cai8jKVtjy0vcGvpvcmGwCKsKu5eXcCd75HjDVKTe9HKTf2kkFkGnJf8E JP+bUpFxsnbMkTYtxs9qoTZEVuo/SC7OypEdLBnzFGl7l5UE7Ug1peyElPX3 KJFOTSq7Wl3NhHn+pwkWUu2rrA2WlrfE5U0dzBl06ZYXLgcJphSZK3yR+G8h 3Xaq5rpLi2prHRbLtiwQmhH8yC431/oaGZEK2nBMvsQxnXOiThilQsS/IImF RzPlHTeSbCBzD/RnBnJgdz0QWy1GTHtvtOabLVs++vif7GYymNQNySjFH1iZ MICUFQrPpHIcSoY9R1WtvwAJajK33ESStpvjbYF8CZT8IhnsomkO1Qtyh7LH 4JpnyhYrq99YWf3Wf//70EtQF0d0XSul+wmFzaAABVUSks5zzB506pCko5h5 ySQWORctvgjxdpB2HGtIACOPphPY0bttaZ2Xe25Rx77Lk52h9/q5btmxc63N SNIpjLwXstbrIr4dcz8x4B0KnUwTKmTM5GdIfJNHz1QIr08ZhpdC0kOBFEdI tlcXHeF2XO3QZZWIQ3bSc9fV1Tq0pNOEnt2yRL6+C5OOQzgJIkggHrOMNVla b5jL3cREO5Gz9cTFzVB0CZi3eR1+FQNnMwTnMsS+PdqmlyExYrURijTb0ZLN bU12JcMXMiVe5cIjrp1Zm2isg409/TM9APKFtmKl6kqo+kooKlP910oNwm3k +scMXTyrDLGD7E2Q4oDkHB4s/4bevLWg92C9PPW5JCq1Ojz0VnH0Hk7DB7VN nxb2bEoe/SFP4MmW+8VzqHvr5PtqZB2PLgV0UqLwC1X4haCTj/wwxoHKK6K2 a43SXBI0XYRMB4jbOk16byT9LW7lO7dTDwRHxqlV6idJ5vcdfHfGd5AVr63I o79XL9pHmYzumi42wSjewa0Ndpepk/of3yifRjKXXiSfaGaQcJcAdFysIx3K fJDCdfzoP73+6mw96e5OmG+Zl5f3GEl4RCTe4J2VnxZklatgBAUUZndbjUNE 7q7K6cCeJzP8LBJcgiwVlTgRfKlgXD53CagZlH1J5JK/vvsZHigiIvJJkvvz xDWo5NCeljQfQOemOV4trFtvjff68tC+NqQFBemLk8gxqOaDzdcnZ7uv/2q+ 8OhBYUcxfODG9Llcer/lojOWaoTjfppAp2FGtMxiBAOi/cens8X3dw5r6PrT 5eNejIlbg8p6JTKxMIpEq7oapvMLAdnk/AmhFq0SGMK71a4tqmNsbLW9E979 o08+M+u1Ggxcm2c+jx4/ekVjeMjhRUn6EfRY7ZTnxfE7XhPcwtnlUJPa67Y9 rKops0kbnD14KoVzIJ17lDzs0TBxo1/TYBBz4Keb5qgksURbLjSFsNTODMWO CvmWctn+arl3P6TTG6MdP+SRr85mfxDZVizbHiKqDBJbBMizSTALRuRpjmRK MrwmWq9LBF06aTvc/QkUd8GEGgSark5ZVsV4QC7PBUfKkp6k9BFdv96wxXrz DyUDe5jIFor0YM2UF3MmmaNlihEtflsdKwPyNuiPLBZgB5rVdnnSuKsTIykK FHuOJ7iy+Do7piIoQdoWKGm8IW8hyauDJkeaHzQwY0aB9m6XNI8FSQFJu62s /oz7v97VJ1QGKQPadglifCgMxi6GhC+Gq6KPtsABpjLwtrTLV8yreaTufRpJ r9x0mDF9ljVTHS9vDZblnxFV+E2Ody6yHWA68WjGnu1r//7hqo9IP3Ya1E82 wedopiltezCtE3fMs36GFSNnXJPIhpGHmzyNxGwB79YZe6aCOqDjJ0ynHBpL 3jcy0btIyY1VBELebqhxa48XtwYDO3tmERJOJjk/4mTVkBtb29OsbfeXMBLk 2MO5eea+k87V2pbKEsUGLd+YeWj0Z2vePfLjUdDuPCThGyTZDpB+jQIqAyYp PpP8xscfN1i8Pu+iCldqD0MJ01QNmTDBqX7cu2eQsGTI/popN+YMHr7pmjT6 C17ReZFRa3nghqQPSd2NJNiieC0yJx5dQ/WZrAyUTI89cF6oB4/awYtkWvHd NlAZm24oKv0lMp7xxUkQFPNondlZJWeqTfIqDWnrcPYJAStXgS+tWQyjzlTo gpBszNQfH+7VnjpdTpxgxMhNhlnz8bbETsOxytEbxQUYJ0rF1pX5TDWRplDT I6l5NgkufBnaUmQJfJ2MrikliArPi6qDxDy6aTYEI8JI2mTKPoqpH7mv6hQo LUyKw/STZ2v7/FH9jir92QbRRP5paCd2UdAST2kfVQVP6NkkHVJkf+3UhS5l Q7aiI1pGj5HRwuXtJEDaG6DWHpK2wnDDk2NO9iKUAMXgz1gLE1z5sIsBZXXl cGeDriyEHqevCJBLBh5PzXNJdGbsEnPmEGM6PV7WeV0q6jGImzDi/tvrVq/M d7cGbuqTA85rgm4JOpy2+u11X15OjFQAcAsh9ytZamhlsI4RpzAbH0/Nc0lw xQ9odtZNR0RLmnzEyrkn+JVvrMRvYmveeT9i0JQjRO9NmR7kHNVbJrqhPwMa r7+7ejXe7LU33pyeJauDjA2imyGlfhp2uXZR+OeStEqRffRp75BJitekpBN3 FYv6OXzVm3/bRCTtYoFtHRymG33bVSUj8sEBhpnqAVnbIOFzKN0ee8Fm5Zur YqLnNn1emTlh43BISFmAWsRevKh+LonGjF3onDnlL0w9J5B1LFwODoQ/h5fw laEN/Z40/umq/tN36L4F5PjSvCpKYh8l3HA3B2AcwLQwCr9IG76RQwyqv6Uz PuUB4kWeMmIGNcf8ZDfO6qXsue/4ypwegJ50qCZAgYM816U1NyCtiupfx3ak CvbSkONt4M2GzHHg6mHh+seLIMiGSwjuKkYX53gxkma15eiVydP7GmW1rTAQ byo5Z06zx+JsIWk35H0P1d7ATgM1n6eDEgEEdxucG/X7a83fVeqP1s14tiiT RdDb19LpbN1PuC7hPg3khUiUJpP1twde+cNfrhxYbU5bIYt/W5T1GY+yrZN5 nD5IrJYl0NS5jbLYdmnUgCKqTRyWNxQZwU6/1Fl5uKXzGzr7667xtWd/XPG7 3++12Y4YkEVD3CdJSkqKi4t72n9KerX6vTWv4wvB+l9/HKd/SGvaXNh/JF1w LnmSkDrumsF3yuA6ZAw6ZnAd07iO2bzjpaNHq8YPFo8cu809d6U36Az/zlvr PsG7v/HuGo1m0a16VvN1LE5yv6JeVBQK1dnZhdlVIoH+PpQzYGANqZkjqhb8 NbzYa0jVOqpukejqZ/RVSmijsWpcnF0oFMpTcwNQUFAQHh5eVFTk5+cnEome 0XJZhSDIzZs3cTf6+vo8PT1zcnL+XyRVVVUEAqG+vh7DMDxNHh4e+HF4eFg3 J+3yC5+ZeCKoVCqRSMQ9wc/gVHho3BMvL6+rV6/iLuETOHaZFTenoKAg3AES iSSXyx92qaenh0wm4xM4efmFR0lMTMSz0NbWZjIt3I3/A4ILMJU= "], {{0, 46.}, {46., 0}}, {0, 255}, ColorFunction -> RGBColor, ImageResolution -> {72, 72}], BoxForm`ImageTag[ "Byte", ColorSpace -> "RGB", Interleaving -> True, MetaInformation -> Association[ "XMP" -> Association[ "XMPBasicSchema" -> Association[ "CreatorTool" -> "Adobe Photoshop CC 2017 (Macintosh)", "CreateDate" -> DateObject[{2017, 12, 1, 16, 38, 15.}, "Instant", "Gregorian", 1.], "ModifyDate" -> DateObject[{2017, 12, 4, 22, 9, 4.}, "Instant", "Gregorian", 1.], "MetadataDate" -> DateObject[{2017, 12, 4, 22, 9, 4.}, "Instant", "Gregorian", 1.]], "DublinCoreSchema" -> Association["Format" -> "image/png"], "PhotoshopSchema" -> Association["ColorMode" -> 3], "XMPMediaManagementSchema" -> Association[ "InstanceID" -> "xmp.iid:a23149e2-a0d1-4081-bab4-71ed4683843a", "DocumentID" -> "xmp.did:a23149e2-a0d1-4081-bab4-71ed4683843a", "OriginalDocumentID" -> "xmp.did:a23149e2-a0d1-4081-bab4-71ed4683843a", "History[1]" -> Association[ "Event" -> Association[ "Action" -> "created", "InstanceID" -> "xmp.iid:a23149e2-a0d1-4081-bab4-71ed4683843a", "When" -> DateObject[{2017, 12, 1, 16, 38, 15.}, "Instant", "Gregorian", 1.], "SoftwareAgent" -> "Adobe Photoshop CC 2017 (Macintosh)"]]]]]], Selectable -> False], DefaultBaseStyle -> "ImageGraphics", ImageSizeRaw -> {46., 46.}, PlotRange -> {{0, 46.}, {0, 46.}}], GridBox[{{ RowBox[{ TagBox["\"Name: \"", "SummaryItemAnnotation"], "\[InvisibleSpace]", TagBox["\"IGraphM\"", "SummaryItem"]}]}, { RowBox[{ TagBox["\"Version: \"", "SummaryItemAnnotation"], "\[InvisibleSpace]", TagBox["\"0.5.1\"", "SummaryItem"]}]}}, AutoDelete -> False, BaseStyle -> { ShowStringCharacters -> False, NumberMarks -> False, PrintPrecision -> 3, ShowSyntaxStyles -> False}, GridBoxAlignment -> { "Columns" -> {{Left}}, "Rows" -> {{Automatic}}}, GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings -> { "Columns" -> {{2}}, "Rows" -> {{Automatic}}}]}}, AutoDelete -> False, BaselinePosition -> {1, 1}, GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], True -> GridBox[{{ PaneBox[ ButtonBox[ DynamicBox[ FEPrivate`FrontEndResource["FEBitmaps", "SummaryBoxCloser"]], Appearance -> None, BaseStyle -> {}, ButtonFunction :> (Typeset`open$$ = False), Evaluator -> Automatic, Method -> "Preemptive"], Alignment -> {Center, Center}, ImageSize -> Dynamic[{ Automatic, 3.5 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[ Magnification])}]], GraphicsBox[ TagBox[ RasterBox[CompressedData[" 1:eJzFmAdQG1cax5m7ubnMzZXM+O4myTnJ2U4mmUm55HJOgn2xg00cF+KCu42x g2OwMW6iRQZswKaEGmODwPReDKJJdCEQRTQZjEAIiSoJ1ECoSyut9rulnCtu TLj7j7Qjrd5732//33v7vtUqpwv2zr+ysrJyfwU/2H/vbUMgfE/c+yr+Zf95 9zMu50/9sO28xymXU4QvnX6Nn/x44T37Gf4roVDIYDAoc6Ius+aj1NfX83g8 eFQ1NTUBAQHu7u7+/v6BgYEBy6zAOXl5efn4+BQUFOh0uvsYBAIhLi6OxWKN jY0JBIKxl9H4nF62Cx6FzWZnZmZ6eHjgR7PZPDIycvny5YSEBKVSCf9zoSia n5+P56Kjo6OsrMzb23toaGjJo5nMJq1Ws+TuuANhYWGJiYnJyckxMTF6vX5p 48hEoxvWr1u1ek33vbtLhsFtmYchkUgGg2EpQ6g5t4NcrebkRNhlBMGSSSIj I3FPYmNj78/el1D3bVHR+cCK6o32pzau3ZX2U24FJ4hjLlgCSW5ublRU1BJI MJ0Cai8jKVtjy0vcGvpvcmGwCKsKu5eXcCd75HjDVKTe9HKTf2kkFkGnJf8E JP+bUpFxsnbMkTYtxs9qoTZEVuo/SC7OypEdLBnzFGl7l5UE7Ug1peyElPX3 KJFOTSq7Wl3NhHn+pwkWUu2rrA2WlrfE5U0dzBl06ZYXLgcJphSZK3yR+G8h 3Xaq5rpLi2prHRbLtiwQmhH8yC431/oaGZEK2nBMvsQxnXOiThilQsS/IImF RzPlHTeSbCBzD/RnBnJgdz0QWy1GTHtvtOabLVs++vif7GYymNQNySjFH1iZ MICUFQrPpHIcSoY9R1WtvwAJajK33ESStpvjbYF8CZT8IhnsomkO1Qtyh7LH 4JpnyhYrq99YWf3Wf//70EtQF0d0XSul+wmFzaAABVUSks5zzB506pCko5h5 ySQWORctvgjxdpB2HGtIACOPphPY0bttaZ2Xe25Rx77Lk52h9/q5btmxc63N SNIpjLwXstbrIr4dcz8x4B0KnUwTKmTM5GdIfJNHz1QIr08ZhpdC0kOBFEdI tlcXHeF2XO3QZZWIQ3bSc9fV1Tq0pNOEnt2yRL6+C5OOQzgJIkggHrOMNVla b5jL3cREO5Gz9cTFzVB0CZi3eR1+FQNnMwTnMsS+PdqmlyExYrURijTb0ZLN bU12JcMXMiVe5cIjrp1Zm2isg409/TM9APKFtmKl6kqo+kooKlP910oNwm3k +scMXTyrDLGD7E2Q4oDkHB4s/4bevLWg92C9PPW5JCq1Ojz0VnH0Hk7DB7VN nxb2bEoe/SFP4MmW+8VzqHvr5PtqZB2PLgV0UqLwC1X4haCTj/wwxoHKK6K2 a43SXBI0XYRMB4jbOk16byT9LW7lO7dTDwRHxqlV6idJ5vcdfHfGd5AVr63I o79XL9pHmYzumi42wSjewa0Ndpepk/of3yifRjKXXiSfaGaQcJcAdFysIx3K fJDCdfzoP73+6mw96e5OmG+Zl5f3GEl4RCTe4J2VnxZklatgBAUUZndbjUNE 7q7K6cCeJzP8LBJcgiwVlTgRfKlgXD53CagZlH1J5JK/vvsZHigiIvJJkvvz xDWo5NCeljQfQOemOV4trFtvjff68tC+NqQFBemLk8gxqOaDzdcnZ7uv/2q+ 8OhBYUcxfODG9Llcer/lojOWaoTjfppAp2FGtMxiBAOi/cens8X3dw5r6PrT 5eNejIlbg8p6JTKxMIpEq7oapvMLAdnk/AmhFq0SGMK71a4tqmNsbLW9E979 o08+M+u1Ggxcm2c+jx4/ekVjeMjhRUn6EfRY7ZTnxfE7XhPcwtnlUJPa67Y9 rKops0kbnD14KoVzIJ17lDzs0TBxo1/TYBBz4Keb5qgksURbLjSFsNTODMWO CvmWctn+arl3P6TTG6MdP+SRr85mfxDZVizbHiKqDBJbBMizSTALRuRpjmRK MrwmWq9LBF06aTvc/QkUd8GEGgSark5ZVsV4QC7PBUfKkp6k9BFdv96wxXrz DyUDe5jIFor0YM2UF3MmmaNlihEtflsdKwPyNuiPLBZgB5rVdnnSuKsTIykK FHuOJ7iy+Do7piIoQdoWKGm8IW8hyauDJkeaHzQwY0aB9m6XNI8FSQFJu62s /oz7v97VJ1QGKQPadglifCgMxi6GhC+Gq6KPtsABpjLwtrTLV8yreaTufRpJ r9x0mDF9ljVTHS9vDZblnxFV+E2Ody6yHWA68WjGnu1r//7hqo9IP3Ya1E82 wedopiltezCtE3fMs36GFSNnXJPIhpGHmzyNxGwB79YZe6aCOqDjJ0ynHBpL 3jcy0btIyY1VBELebqhxa48XtwYDO3tmERJOJjk/4mTVkBtb29OsbfeXMBLk 2MO5eea+k87V2pbKEsUGLd+YeWj0Z2vePfLjUdDuPCThGyTZDpB+jQIqAyYp PpP8xscfN1i8Pu+iCldqD0MJ01QNmTDBqX7cu2eQsGTI/popN+YMHr7pmjT6 C17ReZFRa3nghqQPSd2NJNiieC0yJx5dQ/WZrAyUTI89cF6oB4/awYtkWvHd NlAZm24oKv0lMp7xxUkQFPNondlZJWeqTfIqDWnrcPYJAStXgS+tWQyjzlTo gpBszNQfH+7VnjpdTpxgxMhNhlnz8bbETsOxytEbxQUYJ0rF1pX5TDWRplDT I6l5NgkufBnaUmQJfJ2MrikliArPi6qDxDy6aTYEI8JI2mTKPoqpH7mv6hQo LUyKw/STZ2v7/FH9jir92QbRRP5paCd2UdAST2kfVQVP6NkkHVJkf+3UhS5l Q7aiI1pGj5HRwuXtJEDaG6DWHpK2wnDDk2NO9iKUAMXgz1gLE1z5sIsBZXXl cGeDriyEHqevCJBLBh5PzXNJdGbsEnPmEGM6PV7WeV0q6jGImzDi/tvrVq/M d7cGbuqTA85rgm4JOpy2+u11X15OjFQAcAsh9ytZamhlsI4RpzAbH0/Nc0lw xQ9odtZNR0RLmnzEyrkn+JVvrMRvYmveeT9i0JQjRO9NmR7kHNVbJrqhPwMa r7+7ejXe7LU33pyeJauDjA2imyGlfhp2uXZR+OeStEqRffRp75BJitekpBN3 FYv6OXzVm3/bRCTtYoFtHRymG33bVSUj8sEBhpnqAVnbIOFzKN0ee8Fm5Zur YqLnNn1emTlh43BISFmAWsRevKh+LonGjF3onDnlL0w9J5B1LFwODoQ/h5fw laEN/Z40/umq/tN36L4F5PjSvCpKYh8l3HA3B2AcwLQwCr9IG76RQwyqv6Uz PuUB4kWeMmIGNcf8ZDfO6qXsue/4ypwegJ50qCZAgYM816U1NyCtiupfx3ak CvbSkONt4M2GzHHg6mHh+seLIMiGSwjuKkYX53gxkma15eiVydP7GmW1rTAQ byo5Z06zx+JsIWk35H0P1d7ATgM1n6eDEgEEdxucG/X7a83fVeqP1s14tiiT RdDb19LpbN1PuC7hPg3khUiUJpP1twde+cNfrhxYbU5bIYt/W5T1GY+yrZN5 nD5IrJYl0NS5jbLYdmnUgCKqTRyWNxQZwU6/1Fl5uKXzGzr7667xtWd/XPG7 3++12Y4YkEVD3CdJSkqKi4t72n9KerX6vTWv4wvB+l9/HKd/SGvaXNh/JF1w LnmSkDrumsF3yuA6ZAw6ZnAd07iO2bzjpaNHq8YPFo8cu809d6U36Az/zlvr PsG7v/HuGo1m0a16VvN1LE5yv6JeVBQK1dnZhdlVIoH+PpQzYGANqZkjqhb8 NbzYa0jVOqpukejqZ/RVSmijsWpcnF0oFMpTcwNQUFAQHh5eVFTk5+cnEome 0XJZhSDIzZs3cTf6+vo8PT1zcnL+XyRVVVUEAqG+vh7DMDxNHh4e+HF4eFg3 J+3yC5+ZeCKoVCqRSMQ9wc/gVHho3BMvL6+rV6/iLuETOHaZFTenoKAg3AES iSSXyx92qaenh0wm4xM4efmFR0lMTMSz0NbWZjIt3I3/A4ILMJU= "], {{0, 46.}, {46., 0}}, {0, 255}, ColorFunction -> RGBColor, ImageResolution -> {72, 72}], BoxForm`ImageTag[ "Byte", ColorSpace -> "RGB", Interleaving -> True, MetaInformation -> Association[ "XMP" -> Association[ "XMPBasicSchema" -> Association[ "CreatorTool" -> "Adobe Photoshop CC 2017 (Macintosh)", "CreateDate" -> DateObject[{2017, 12, 1, 16, 38, 15.}, "Instant", "Gregorian", 1.], "ModifyDate" -> DateObject[{2017, 12, 4, 22, 9, 4.}, "Instant", "Gregorian", 1.], "MetadataDate" -> DateObject[{2017, 12, 4, 22, 9, 4.}, "Instant", "Gregorian", 1.]], "DublinCoreSchema" -> Association["Format" -> "image/png"], "PhotoshopSchema" -> Association["ColorMode" -> 3], "XMPMediaManagementSchema" -> Association[ "InstanceID" -> "xmp.iid:a23149e2-a0d1-4081-bab4-71ed4683843a", "DocumentID" -> "xmp.did:a23149e2-a0d1-4081-bab4-71ed4683843a", "OriginalDocumentID" -> "xmp.did:a23149e2-a0d1-4081-bab4-71ed4683843a", "History[1]" -> Association[ "Event" -> Association[ "Action" -> "created", "InstanceID" -> "xmp.iid:a23149e2-a0d1-4081-bab4-71ed4683843a", "When" -> DateObject[{2017, 12, 1, 16, 38, 15.}, "Instant", "Gregorian", 1.], "SoftwareAgent" -> "Adobe Photoshop CC 2017 (Macintosh)"]]]]]], Selectable -> False], DefaultBaseStyle -> "ImageGraphics", ImageSizeRaw -> {46., 46.}, PlotRange -> {{0, 46.}, {0, 46.}}], GridBox[{{ RowBox[{ TagBox["\"Name: \"", "SummaryItemAnnotation"], "\[InvisibleSpace]", TagBox["\"IGraphM\"", "SummaryItem"]}]}, { RowBox[{ TagBox["\"Version: \"", "SummaryItemAnnotation"], "\[InvisibleSpace]", TagBox["\"0.5.1\"", "SummaryItem"]}]}, { RowBox[{ TagBox["\"Location: \"", "SummaryItemAnnotation"], "\[InvisibleSpace]", TagBox[ "\"C:\\\\Users\\\\Emilie \ Rivkin\\\\AppData\\\\Roaming\\\\Mathematica\\\\Paclets\\\\Repository\\\\\ IGraphM-0.5.1\"", "SummaryItem"]}]}, { RowBox[{ TagBox["\"Description: \"", "SummaryItemAnnotation"], "\[InvisibleSpace]", TagBox[ TagBox[ "\"IGraph/M \[Dash] the igraph interface for Mathematica.\ \"", Short], "SummaryItem"]}]}}, AutoDelete -> False, BaseStyle -> { ShowStringCharacters -> False, NumberMarks -> False, PrintPrecision -> 3, ShowSyntaxStyles -> False}, GridBoxAlignment -> { "Columns" -> {{Left}}, "Rows" -> {{Automatic}}}, GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings -> { "Columns" -> {{2}}, "Rows" -> {{Automatic}}}]}}, AutoDelete -> False, BaselinePosition -> {1, 1}, GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}]}, Dynamic[Typeset`open$$], ImageSize -> Automatic]}, "SummaryPanel"], DynamicModuleValues:>{}], "]"}], PacletObject[ Association[ "Name" -> "IGraphM", "Version" -> "0.5.1", "MathematicaVersion" -> "10.0+", "Description" -> "IGraph/M \[Dash] the igraph interface for Mathematica.", "Creator" -> "Szabolcs Horv\[AAcute]t ", "URL" -> "http://szhorvat.net/mathematica/IGraphM", "Thumbnail" -> "Logo.png", "Icon" -> "Logo.png", "Keywords" -> {"igraph", "graph theory", "network analysis"}, "SystemID" -> { "MacOSX-x86-64", "Windows-x86-64", "Linux-x86-64", "Linux-ARM"}, "Extensions" -> {{"Kernel", "Root" -> ".", "Context" -> "IGraphM`"}, { "LibraryLink"}, { "Documentation", "MainPage" -> "Tutorials/IGDocumentation"}}, "Location" -> "C:\\Users\\Emilie \ Rivkin\\AppData\\Roaming\\Mathematica\\Paclets\\Repository\\IGraphM-0.5.1"]], Editable->False, SelectWithContents->True, Selectable->False], "\[InvisibleSpace]", "\<\".\"\>"}], SequenceForm["Installing IGraph/M is complete: ", PacletObject[ Association[ "Name" -> "IGraphM", "Version" -> "0.5.1", "MathematicaVersion" -> "10.0+", "Description" -> "IGraph/M \[Dash] the igraph interface for Mathematica.", "Creator" -> "Szabolcs Horv\[AAcute]t ", "URL" -> "http://szhorvat.net/mathematica/IGraphM", "Thumbnail" -> "Logo.png", "Icon" -> "Logo.png", "Keywords" -> {"igraph", "graph theory", "network analysis"}, "SystemID" -> { "MacOSX-x86-64", "Windows-x86-64", "Linux-x86-64", "Linux-ARM"}, "Extensions" -> {{"Kernel", "Root" -> ".", "Context" -> "IGraphM`"}, { "LibraryLink"}, { "Documentation", "MainPage" -> "Tutorials/IGDocumentation"}}, "Location" -> "C:\\Users\\Emilie \ Rivkin\\AppData\\Roaming\\Mathematica\\Paclets\\Repository\\IGraphM-0.5.1"]], "."], Editable->False]], "Print", CellChangeTimes->{3.832151635828127*^9}, CellLabel-> "During evaluation of \ In[5]:=",ExpressionUUID->"5d32e2af-05fa-4461-8796-9099e2115a5e"], Cell[BoxData[ InterpretationBox[ RowBox[{"\<\"It can now be loaded using the command \"\>", "\[InvisibleSpace]", ButtonBox[ RowBox[{"<<", "\<\"IGraphM`\"\>"}], Appearance->None, BaseStyle->"Link", ButtonFunction:>(FrontEndExecute[{ FrontEnd`SelectionMove[ FrontEnd`EvaluationCell[], After, CellGroup], FrontEnd`NotebookWrite[ FrontEnd`EvaluationNotebook[], #, All], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`EvaluationNotebook[]]}]& ), Evaluator->None, Method->"Preemptive"]}], SequenceForm["It can now be loaded using the command ", Button[ Defer[ Get["IGraphM`"]], FrontEndExecute[{ FrontEnd`SelectionMove[ FrontEnd`EvaluationCell[], After, CellGroup], FrontEnd`NotebookWrite[ FrontEnd`EvaluationNotebook[], #, All], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`EvaluationNotebook[]]}]& , Evaluator -> None, Appearance -> None, BaseStyle -> "Link"]], Editable->False]], "Print", CellChangeTimes->{3.8321516359364223`*^9}, CellLabel-> "During evaluation of \ In[5]:=",ExpressionUUID->"510e29d7-e907-4147-8d8b-fccc5c0f2dde"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"<<", "IGraphM`"}]], "Input", CellChangeTimes->{{3.8321516420783434`*^9, 3.832151645302351*^9}}, CellLabel->"In[6]:=",ExpressionUUID->"8f83865d-4965-40c5-8bad-4548bbcd09d9"], Cell[BoxData[ TemplateBox[{ "IGDocumentation", "shdw", "\"Symbol \\!\\(\\*RowBox[{\\\"\\\\\\\"IGDocumentation\\\\\\\"\\\"}]\\) \ appears in multiple contexts \\!\\(\\*RowBox[{\\\"{\\\", \ RowBox[{\\\"\\\\\\\"IGraphM`\\\\\\\"\\\", \\\",\\\", \ \\\"\\\\\\\"Global`\\\\\\\"\\\"}], \\\"}\\\"}]\\); definitions in context \\!\ \\(\\*RowBox[{\\\"\\\\\\\"IGraphM`\\\\\\\"\\\"}]\\) may shadow or be shadowed \ by other definitions.\"", 2, 6, 5, 26291035970162241021, "Local", "IGraphM`IGDocumentation"}, "MessageTemplate2"]], "Message", "MSG", CellChangeTimes->{3.8321516462852325`*^9}, CellLabel-> "During evaluation of \ In[6]:=",ExpressionUUID->"89d96776-46a4-4a8f-94d2-82872e013c08"], Cell[BoxData[ TagBox[GridBox[{ {"\<\"IGraph/M 0.5.1 (October 12, 2020)\"\>"}, {"\<\"Evaluate \\!\\(\\*ButtonBox[\\\"IGDocumentation[]\\\",BaseStyle->\\\ \"Link\\\",ButtonData->\\\"paclet:IGraphM\\\"]\\) to get started.\"\>"} }, DefaultBaseStyle->"Column", GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Column"]], "Output", CellChangeTimes->{3.8321516533863616`*^9}, CellLabel->"Out[6]=",ExpressionUUID->"a3a99bb6-9bd7-4e76-a352-31154db4eb73"] }, Open ]], Cell[BoxData[ RowBox[{"IGDocumentation", "[", "]"}]], "Input", CellChangeTimes->{{3.8321516567464046`*^9, 3.8321516618620677`*^9}}, CellLabel->"In[7]:=",ExpressionUUID->"0ea0ed7d-9f23-4291-a21c-09d5c95a9618"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"Graph", "[", RowBox[{ RowBox[{"GraphData", "[", "\"\\"", "]"}], ",", RowBox[{"EdgeStyle", "->", RowBox[{"Directive", "[", RowBox[{"Thick", ",", RowBox[{"Opacity", "[", "1", "]"}]}], "]"}]}], ",", RowBox[{"VertexStyle", "->", "Black"}]}], "]"}], "//", RowBox[{"IGEdgeMap", "[", RowBox[{ RowBox[{"ColorData", "[", "109", "]"}], ",", RowBox[{"EdgeStyle", "->", "IGEdgeColoring"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.8321516953889093`*^9, 3.8321516954132996`*^9}}, CellLabel->"In[8]:=",ExpressionUUID->"51e42d7b-5dd8-4cea-ae46-9aa90b09347c"], Cell[BoxData[ GraphicsBox[ NamespaceBox["NetworkGraphics", DynamicModuleBox[{Typeset`graph = HoldComplete[ Graph[{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}, {Null, SparseArray[ Automatic, {20, 20}, 0, { 1, {{0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60}, {{14}, {15}, {16}, {5}, {6}, {13}, {7}, {14}, { 19}, {8}, {15}, {20}, {2}, {11}, {19}, {2}, {12}, {20}, {3}, {11}, { 16}, {4}, {12}, {16}, {10}, {14}, {17}, {9}, {15}, {18}, {5}, {7}, { 12}, {6}, {8}, {11}, {2}, {17}, {18}, {1}, {3}, {9}, {1}, {4}, { 10}, {1}, {7}, {8}, {9}, {13}, {19}, {10}, {13}, {20}, {3}, {5}, { 17}, {4}, {6}, {18}}}, Pattern}]}, {EdgeStyle -> { Directive[ Thickness[Large], Opacity[1]], UndirectedEdge[18, 20] -> RGBColor[0., 0.742291, 0.873126], UndirectedEdge[1, 14] -> RGBColor[1., 0.4, 0.], UndirectedEdge[7, 16] -> RGBColor[1., 0.4, 0.], UndirectedEdge[5, 19] -> RGBColor[1., 0.656408, 0.], UndirectedEdge[2, 13] -> RGBColor[0.655728, 0.8, 0.], UndirectedEdge[6, 20] -> RGBColor[0.655728, 0.8, 0.], UndirectedEdge[9, 14] -> RGBColor[0.655728, 0.8, 0.], UndirectedEdge[4, 20] -> RGBColor[1., 0.4, 0.], UndirectedEdge[3, 14] -> RGBColor[0., 0.742291, 0.873126], UndirectedEdge[11, 12] -> RGBColor[0.655728, 0.8, 0.], UndirectedEdge[2, 6] -> RGBColor[1., 0.4, 0.], UndirectedEdge[1, 15] -> RGBColor[0., 0.742291, 0.873126], UndirectedEdge[4, 15] -> RGBColor[0.655728, 0.8, 0.], UndirectedEdge[4, 8] -> RGBColor[1., 0.656408, 0.], UndirectedEdge[8, 16] -> RGBColor[0., 0.742291, 0.873126], UndirectedEdge[8, 12] -> RGBColor[1., 0.4, 0.], UndirectedEdge[1, 16] -> RGBColor[0.655728, 0.8, 0.], UndirectedEdge[3, 19] -> RGBColor[1., 0.4, 0.], UndirectedEdge[13, 17] -> RGBColor[0., 0.742291, 0.873126], UndirectedEdge[13, 18] -> RGBColor[1., 0.4, 0.], UndirectedEdge[5, 11] -> RGBColor[1., 0.4, 0.], UndirectedEdge[9, 17] -> RGBColor[1., 0.4, 0.], UndirectedEdge[6, 12] -> RGBColor[0., 0.742291, 0.873126], UndirectedEdge[10, 15] -> RGBColor[1., 0.4, 0.], UndirectedEdge[3, 7] -> RGBColor[0.655728, 0.8, 0.], UndirectedEdge[9, 10] -> RGBColor[0., 0.742291, 0.873126], UndirectedEdge[2, 5] -> RGBColor[0., 0.742291, 0.873126], UndirectedEdge[10, 18] -> RGBColor[0.655728, 0.8, 0.], UndirectedEdge[17, 19] -> RGBColor[0.655728, 0.8, 0.], UndirectedEdge[7, 11] -> RGBColor[0., 0.742291, 0.873126]}, GraphLayout -> {"Dimension" -> 2}, VertexCoordinates -> CompressedData[" 1:eJxTTMoPSmViYGAQAWIQ/SP48dLZR37Y12ftKZks8cB+33wp/bsqn/ZHpVjf 9++9vp8BCuxN43Z58vyyt9xyomzf/Hf2QMnpeUJf90P174fph8rvh8nD9L+r AZnA7HCyDGTDd/s3gTvkWl//398udvPc9+DLUH237DfNfb/8mPd9e3VDjjUy UUf2H/6qEdN/iOnAn5UfL/kmvbA3BoPv+2H6oer3w9SngcEz+4dVIuvcH76z DwE5T+GTPUsYn+6muddh5jnAzIPavx9mP8y9y4C6NhQ9gJm3H2YeTB7iv8/7 AVLKoH4= "], VertexStyle -> { GrayLevel[0]}}]]}, TagBox[GraphicsGroupBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAQAWIQ/SP48dLZR37Y12ftKZks8cB+33wp/bsqn/ZHpVjf 9++9vp8BCuxN43Z58vyyt9xyomzf/Hf2QMnpeUJf90P174fph8rvh8nD9L+r AZnA7HCyDGTDd/s3gTvkWl//398udvPc9+DLUH237DfNfb/8mPd9e3VDjjUy UUf2H/6qEdN/iOnAn5UfL/kmvbA3BoPv+2H6oer3w9SngcEz+4dVIuvcH76z DwE5T+GTPUsYn+6muddh5jnAzIPavx9mP8y9y4C6NhQ9gJm3H2YeTB7iv8/7 AVLKoH4= "], { {Hue[0.6, 0.7, 0.5], Thickness[Large], Opacity[1], {RGBColor[1., 0.4, 0.], {Arrowheads[0.], ArrowBox[{1, 14}, 0.0412452419793366]}}, {RGBColor[0., 0.742291, 0.873126], {Arrowheads[0.], ArrowBox[{1, 15}, 0.0412452419793366]}}, {RGBColor[0.655728, 0.8, 0.], {Arrowheads[0.], ArrowBox[{1, 16}, 0.0412452419793366]}}, {RGBColor[0., 0.742291, 0.873126], {Arrowheads[0.], ArrowBox[{2, 5}, 0.0412452419793366]}}, {RGBColor[1., 0.4, 0.], {Arrowheads[0.], ArrowBox[{2, 6}, 0.0412452419793366]}}, {RGBColor[0.655728, 0.8, 0.], {Arrowheads[0.], ArrowBox[{2, 13}, 0.0412452419793366]}}, {RGBColor[0.655728, 0.8, 0.], {Arrowheads[0.], ArrowBox[{3, 7}, 0.0412452419793366]}}, {RGBColor[0., 0.742291, 0.873126], {Arrowheads[0.], ArrowBox[{3, 14}, 0.0412452419793366]}}, {RGBColor[1., 0.4, 0.], {Arrowheads[0.], ArrowBox[{3, 19}, 0.0412452419793366]}}, {RGBColor[1., 0.656408, 0.], {Arrowheads[0.], ArrowBox[{4, 8}, 0.0412452419793366]}}, {RGBColor[0.655728, 0.8, 0.], {Arrowheads[0.], ArrowBox[{4, 15}, 0.0412452419793366]}}, {RGBColor[1., 0.4, 0.], {Arrowheads[0.], ArrowBox[{4, 20}, 0.0412452419793366]}}, {RGBColor[1., 0.4, 0.], {Arrowheads[0.], ArrowBox[{5, 11}, 0.0412452419793366]}}, {RGBColor[1., 0.656408, 0.], {Arrowheads[0.], ArrowBox[{5, 19}, 0.0412452419793366]}}, {RGBColor[0., 0.742291, 0.873126], {Arrowheads[0.], ArrowBox[{6, 12}, 0.0412452419793366]}}, {RGBColor[0.655728, 0.8, 0.], {Arrowheads[0.], ArrowBox[{6, 20}, 0.0412452419793366]}}, {RGBColor[0., 0.742291, 0.873126], {Arrowheads[0.], ArrowBox[{7, 11}, 0.0412452419793366]}}, {RGBColor[1., 0.4, 0.], {Arrowheads[0.], ArrowBox[{7, 16}, 0.0412452419793366]}}, {RGBColor[1., 0.4, 0.], {Arrowheads[0.], ArrowBox[{8, 12}, 0.0412452419793366]}}, {RGBColor[0., 0.742291, 0.873126], {Arrowheads[0.], ArrowBox[{8, 16}, 0.0412452419793366]}}, {RGBColor[0., 0.742291, 0.873126], {Arrowheads[0.], ArrowBox[{9, 10}, 0.0412452419793366]}}, {RGBColor[0.655728, 0.8, 0.], {Arrowheads[0.], ArrowBox[{9, 14}, 0.0412452419793366]}}, {RGBColor[1., 0.4, 0.], {Arrowheads[0.], ArrowBox[{9, 17}, 0.0412452419793366]}}, {RGBColor[1., 0.4, 0.], {Arrowheads[0.], ArrowBox[{10, 15}, 0.0412452419793366]}}, {RGBColor[0.655728, 0.8, 0.], {Arrowheads[0.], ArrowBox[{10, 18}, 0.0412452419793366]}}, {RGBColor[0.655728, 0.8, 0.], {Arrowheads[0.], ArrowBox[{11, 12}, 0.0412452419793366]}}, {RGBColor[0., 0.742291, 0.873126], {Arrowheads[0.], ArrowBox[{13, 17}, 0.0412452419793366]}}, {RGBColor[1., 0.4, 0.], {Arrowheads[0.], ArrowBox[{13, 18}, 0.0412452419793366]}}, {RGBColor[0.655728, 0.8, 0.], {Arrowheads[0.], ArrowBox[{17, 19}, 0.0412452419793366]}}, {RGBColor[0., 0.742291, 0.873126], {Arrowheads[0.], ArrowBox[{18, 20}, 0.0412452419793366]}}}, {GrayLevel[0], EdgeForm[{GrayLevel[0], Opacity[0.7]}], DiskBox[1, 0.0412452419793366], DiskBox[2, 0.0412452419793366], DiskBox[3, 0.0412452419793366], DiskBox[4, 0.0412452419793366], DiskBox[5, 0.0412452419793366], DiskBox[6, 0.0412452419793366], DiskBox[7, 0.0412452419793366], DiskBox[8, 0.0412452419793366], DiskBox[9, 0.0412452419793366], DiskBox[10, 0.0412452419793366], DiskBox[11, 0.0412452419793366], DiskBox[12, 0.0412452419793366], DiskBox[13, 0.0412452419793366], DiskBox[14, 0.0412452419793366], DiskBox[15, 0.0412452419793366], DiskBox[16, 0.0412452419793366], DiskBox[17, 0.0412452419793366], DiskBox[18, 0.0412452419793366], DiskBox[19, 0.0412452419793366], DiskBox[20, 0.0412452419793366]}}]], MouseAppearanceTag["NetworkGraphics"]], AllowKernelInitialization->False]], DefaultBaseStyle->{ "NetworkGraphics", FrontEnd`GraphicsHighlightColor -> Hue[0.8, 1., 0.6]}, FormatType->TraditionalForm, FrameTicks->None]], "Output", CellChangeTimes->{3.83215170619855*^9}, CellLabel->"Out[8]=",ExpressionUUID->"280a74ae-016d-433f-ae26-c90945eee3bc"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"g", "=", RowBox[{"IGTriangularLattice", "[", RowBox[{"3", ",", RowBox[{"VertexShapeFunction", "->", "\"\\""}]}], "]"}]}]], "Input", CellChangeTimes->{{3.8321517428542757`*^9, 3.8321517428862677`*^9}}, CellLabel->"In[9]:=",ExpressionUUID->"570405f9-cea4-4018-bd71-20995bb7d8e5"], Cell[BoxData[ GraphicsBox[ NamespaceBox["NetworkGraphics", DynamicModuleBox[{Typeset`graph = HoldComplete[ Graph[{1, 2, 3, 4, 5, 6}, { Null, {{1, 2}, {1, 3}, {2, 3}, {2, 4}, {2, 5}, {4, 5}, {3, 5}, {3, 6}, { 5, 6}}}, {VertexShapeFunction -> {"Name"}, VertexCoordinates -> {{ Rational[1, 2], 3^Rational[1, 2]}, { 0, Rational[1, 2] 3^Rational[1, 2]}, { 1, Rational[1, 2] 3^Rational[1, 2]}, { Rational[-1, 2], 0}, { Rational[1, 2], 0}, { Rational[3, 2], 0}}}]]}, TagBox[ GraphicsGroupBox[ GraphicsComplexBox[{{0.5, 1.7320508075688772`}, {0., 0.8660254037844386}, {1., 0.8660254037844386}, {-0.5, 0.}, {0.5, 0.}, { 1.5, 0.}}, { {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[0.], ArrowBox[{{1, 2}, {1, 3}, {2, 3}, {2, 4}, {2, 5}, {3, 5}, {3, 6}, {4, 5}, {5, 6}}, 0.04522292993630572]}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], InsetBox[ PaneBox["1", Alignment->Center, ImageMargins->2], 1, BaseStyle->"Graphics"], InsetBox[ PaneBox["2", Alignment->Center, ImageMargins->2], 2, BaseStyle->"Graphics"], InsetBox[ PaneBox["3", Alignment->Center, ImageMargins->2], 3, BaseStyle->"Graphics"], InsetBox[ PaneBox["4", Alignment->Center, ImageMargins->2], 4, BaseStyle->"Graphics"], InsetBox[ PaneBox["5", Alignment->Center, ImageMargins->2], 5, BaseStyle->"Graphics"], InsetBox[ PaneBox["6", Alignment->Center, ImageMargins->2], 6, BaseStyle->"Graphics"]}}]], MouseAppearanceTag["NetworkGraphics"]], AllowKernelInitialization->False]], DefaultBaseStyle->{ "NetworkGraphics", FrontEnd`GraphicsHighlightColor -> Hue[0.8, 1., 0.6]}, FormatType->TraditionalForm, FrameTicks->None]], "Output", CellChangeTimes->{3.8321517441219225`*^9}, CellLabel->"Out[9]=",ExpressionUUID->"e3608828-45a9-48a3-82d1-f495941c3684"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"IGFaces", "[", "g", "]"}], "\[IndentingNewLine]", RowBox[{"IGDualGraph", "[", "g", "]"}]}], "Input", CellChangeTimes->{{3.8321517520638323`*^9, 3.832151759928732*^9}}, CellLabel->"In[10]:=",ExpressionUUID->"327e16cd-3ee9-4db6-971c-83ea808b2811"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "2", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "3", ",", "6", ",", "5", ",", "4", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "4", ",", "5"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "5", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"3", ",", "5", ",", "6"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.8321517608203707`*^9}, CellLabel->"Out[10]=",ExpressionUUID->"35f88189-eb85-4dc8-9379-aaea1f17764f"], Cell[BoxData[ GraphicsBox[ NamespaceBox["NetworkGraphics", DynamicModuleBox[{Typeset`graph = HoldComplete[ Graph[{1, 2, 3, 4, 5}, { Null, {{1, 2}, {3, 2}, {1, 4}, {4, 3}, {5, 4}, {2, 5}}}]]}, TagBox[ GraphicsGroupBox[ GraphicsComplexBox[{{0.0009444997846095315, 1.2196160005793895`}, { 0.7208486537844787, 0.9516650322471987}, {0., 0.}, {0.7203374199549782, 0.2676806929720096}, {1.6523889265852785`, 0.6091081184290094}}, { {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[0.], ArrowBox[{{1, 2}, {1, 4}, {2, 3}, {2, 5}, {3, 4}, {4, 5}}, 0.019727114811646074`]}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], DiskBox[1, 0.019727114811646074], DiskBox[2, 0.019727114811646074], DiskBox[3, 0.019727114811646074], DiskBox[4, 0.019727114811646074], DiskBox[5, 0.019727114811646074]}}]], MouseAppearanceTag["NetworkGraphics"]], AllowKernelInitialization->False]], DefaultBaseStyle->{ "NetworkGraphics", FrontEnd`GraphicsHighlightColor -> Hue[0.8, 1., 0.6]}, FormatType->TraditionalForm, FrameTicks->None]], "Output", CellChangeTimes->{3.832151760902153*^9}, CellLabel->"Out[11]=",ExpressionUUID->"0783fc8a-c210-4dee-bf52-f2d394f0efd1"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"PlanarGraph", "[", RowBox[{"IGDualGraph", "[", RowBox[{"g", ",", RowBox[{"VertexLabels", "\[Rule]", "\"\\""}]}], "]"}], "]"}]], "Input", CellChangeTimes->{{3.8321517641545687`*^9, 3.832151773926792*^9}, { 3.8321518311213627`*^9, 3.832151836084566*^9}}, CellLabel->"In[13]:=",ExpressionUUID->"fb51fdc0-b4b8-4e35-a730-47920cc7a454"], Cell[BoxData[ GraphicsBox[ NamespaceBox["NetworkGraphics", DynamicModuleBox[{Typeset`graph = HoldComplete[ Graph[{1, 2, 3, 4, 5}, { Null, {{1, 2}, {3, 2}, {1, 4}, {4, 3}, {5, 4}, {2, 5}}}, { GraphLayout -> "TutteEmbedding", VertexLabels -> {"Name"}}]]}, TagBox[GraphicsGroupBox[{ {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[0.], ArrowBox[{{{-1.8369701987210297`*^-16, 1.}, {1., 1.2246467991473532`*^-16}}, {{-1.8369701987210297`*^-16, 1.}, {-1., -2.4492935982947064`*^-16}}, {{1., 1.2246467991473532`*^-16}, {0., -6.123233995736766*^-17}}, {{1., 1.2246467991473532`*^-16}, {6.123233995736766*^-17, -1.}}, {{ 0., -6.123233995736766*^-17}, {-1., -2.4492935982947064`*^-16}}, \ {{-1., -2.4492935982947064`*^-16}, {6.123233995736766*^-17, -1.}}}, 0.02261146496815286]}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[ 0.7]}], {DiskBox[{-1.8369701987210297*^-16, 1.}, 0.02261146496815286], InsetBox["1", Offset[{2, 2}, {0.022611464968152677, 1.0226114649681528}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{1., 1.2246467991473532*^-16}, 0.02261146496815286], InsetBox["2", Offset[{2, 2}, {1.0226114649681528, 0.022611464968152983}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{0., -6.123233995736766*^-17}, 0.02261146496815286], InsetBox["3", Offset[{2, 2}, {0.02261146496815286, 0.0226114649681528}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{-1., -2.4492935982947064*^-16}, 0.02261146496815286], InsetBox["4", Offset[{2, 2}, {-0.9773885350318472, 0.022611464968152615}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{6.123233995736766*^-17, -1.}, 0.02261146496815286], InsetBox["5", Offset[{2, 2}, {0.022611464968152924, -0.9773885350318472}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}}}], MouseAppearanceTag["NetworkGraphics"]], AllowKernelInitialization->False]], DefaultBaseStyle->{ "NetworkGraphics", FrontEnd`GraphicsHighlightColor -> Hue[0.8, 1., 0.6]}, FormatType->TraditionalForm, FrameTicks->None]], "Output", CellChangeTimes->{3.8321517749291897`*^9, 3.8321518370273714`*^9}, CellLabel->"Out[13]=",ExpressionUUID->"2298d2cc-a87b-459b-92cc-91f57c80e872"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"adjv7f81", "=", RowBox[{"Normal", "[", RowBox[{"AdjacencyMatrix", "[", RowBox[{"{", RowBox[{ RowBox[{"1", "\[UndirectedEdge]", "2"}], ",", RowBox[{"2", "\[UndirectedEdge]", "3"}], ",", RowBox[{"3", "\[UndirectedEdge]", "4"}], ",", RowBox[{"1", "\[UndirectedEdge]", "4"}], ",", RowBox[{"5", "\[UndirectedEdge]", "6"}], ",", RowBox[{"6", "\[UndirectedEdge]", "7"}], ",", RowBox[{"5", "\[UndirectedEdge]", "7"}], ",", RowBox[{"1", "\[UndirectedEdge]", "5"}], ",", RowBox[{"1", "\[UndirectedEdge]", "7"}], ",", RowBox[{"4", "\[UndirectedEdge]", "7"}], ",", RowBox[{"3", "\[UndirectedEdge]", "6"}], ",", RowBox[{"3", "\[UndirectedEdge]", "7"}], ",", RowBox[{"2", "\[UndirectedEdge]", "6"}]}], "}"}], "]"}], "]"}]}]], "Input", CellLabel->"In[14]:=",ExpressionUUID->"fbe79ba7-14a6-45d3-8833-f61300e84e0e"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1", ",", "0", ",", "1", ",", "1", ",", "0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0", ",", "1", ",", "0", ",", "0", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0", ",", "1", ",", "0", ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0", ",", "1", ",", "0", ",", "0", ",", "0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0", ",", "0", ",", "0", ",", "0", ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "1", ",", "0", ",", "1", ",", "0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0", ",", "1", ",", "1", ",", "1", ",", "1", ",", "0"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.8321519460447617`*^9}, CellLabel->"Out[14]=",ExpressionUUID->"a79ec2f5-4b2d-4b53-9c75-548d2f881696"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"adjv7f81g", "=", RowBox[{"PlanarGraph", "[", RowBox[{"AdjacencyGraph", "[", RowBox[{"adjv7f81", ",", RowBox[{"VertexLabels", "\[Rule]", "\"\\""}]}], "]"}], "]"}]}]], "Input", CellChangeTimes->{{3.8321520180017023`*^9, 3.832152020410676*^9}}, CellLabel->"In[16]:=",ExpressionUUID->"77197402-7fe7-49d7-a4df-2184ff05418a"], Cell[BoxData[ GraphicsBox[ NamespaceBox["NetworkGraphics", DynamicModuleBox[{Typeset`graph = HoldComplete[ Graph[{1, 2, 3, 4, 5, 6, 7}, { Null, {{1, 2}, {1, 4}, {1, 5}, {1, 7}, {2, 3}, {2, 6}, {3, 4}, {3, 6}, { 3, 7}, {4, 7}, {5, 6}, {5, 7}, {6, 7}}}, { GraphLayout -> "TutteEmbedding", VertexLabels -> {"Name"}}]]}, TagBox[GraphicsGroupBox[{ {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[0.], ArrowBox[CompressedData[" 1:eJxTTMoPSmVmYGDgBWImKObqmudjWblqDwMYfLCH0ewxIsZqyxbaoMvnbovc n+YyzZ6x/WyZrtglexz690P0b9yDLi9X3mMXXnV4f1qIyGtNp2kY9i0rDXu/ 7/Jpe6vIdbsYnI/tR5eH0BNtYPagq0d3H7o8If3o7kM3D4f74f5FNx9dHl0/ unp0eQDV45Ww "], 0.02261146496815286]}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[ 0.7]}], {DiskBox[{-1.8369701987210297*^-16, 1.}, 0.02261146496815286], InsetBox["1", Offset[{2, 2}, {0.022611464968152677, 1.0226114649681528}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{1., 1.2246467991473532*^-16}, 0.02261146496815286], InsetBox["2", Offset[{2, 2}, {1.0226114649681528, 0.022611464968152983}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{0.21739947019970635, -0.1739197646645126}, 0.02261146496815286], InsetBox["3", Offset[{2, 2}, {0.2400109351678592, -0.15130829969635973}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{0.02174530547056579, 0.28260361291732755}, 0.02261146496815286], InsetBox["4", Offset[{2, 2}, {0.04435677043871865, 0.3052150778854804}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{-1., -2.4492935982947064*^-16}, 0.02261146496815286], InsetBox["5", Offset[{2, 2}, {-0.9773885350318472, 0.022611464968152615}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{6.123233995736766*^-17, -1.}, 0.02261146496815286], InsetBox["6", Offset[{2, 2}, {0.022611464968152924, -0.9773885350318472}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{-0.15217104486594563, 0.021736769650562947}, 0.02261146496815286], InsetBox["7", Offset[{2, 2}, {-0.12955957989779276, 0.04434823461871581}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}}}], MouseAppearanceTag["NetworkGraphics"]], AllowKernelInitialization->False]], DefaultBaseStyle->{ "NetworkGraphics", FrontEnd`GraphicsHighlightColor -> Hue[0.8, 1., 0.6]}, FormatType->TraditionalForm, FrameTicks->None]], "Output", CellChangeTimes->{3.832151963620017*^9, 3.8321520265765657`*^9}, CellLabel->"Out[16]=",ExpressionUUID->"b788abdc-4b95-46b8-a744-2c76ccc02d73"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"AdjacencyGraph", "[", RowBox[{"adjv7f81", ",", RowBox[{"VertexLabels", "\[Rule]", "\"\\""}]}], "]"}]], "Input", CellChangeTimes->{{3.8321523302647347`*^9, 3.8321523484139996`*^9}}, CellLabel->"In[20]:=",ExpressionUUID->"b71c9604-f901-4019-a986-e0e35b58486a"], Cell[BoxData[ GraphicsBox[ NamespaceBox["NetworkGraphics", DynamicModuleBox[{Typeset`graph = HoldComplete[ Graph[{1, 2, 3, 4, 5, 6, 7}, {Null, SparseArray[ Automatic, {7, 7}, 0, { 1, {{0, 4, 7, 11, 14, 17, 21, 26}, {{2}, {4}, {5}, {7}, {1}, {3}, { 6}, {2}, {4}, {6}, {7}, {1}, {3}, {7}, {1}, {6}, {7}, {2}, {3}, { 5}, {7}, {1}, {3}, {4}, {5}, {6}}}, Pattern}]}, { VertexLabels -> {"Name"}}]]}, TagBox[GraphicsGroupBox[{ {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[0.], ArrowBox[CompressedData[" 1:eJxTTMoPSmVmYGDgBWImKL4us1J/yvR39vOzToS7iH+yv34rjMvF4b09AxSg y0s0Baje8ftnv+vt1M9Sor/s0eVh+i7xax7e3/sTQ3758dgSCct39udKS6M5 WX5j2Leu7bDi8tIf9iGS31h+9D3HkA/YUvw2IPymPVtGVCHP42f26OrR3Ycu T0g/uvvQzUOXR/cvuvno8uj60dWjywMAC9W0qA== "], 0.021747623258421556`]}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[ 0.7]}], { DiskBox[{0.9560032778616926, 1.1306804112452153}, 0.021747623258421556], InsetBox["1", Offset[{2, 2}, {0.9777509011201142, 1.1524280345036368}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{0.9765949441851615, 0.}, 0.021747623258421556], InsetBox["2", Offset[{2, 2}, {0.9983425674435831, 0.021747623258421556}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{1.5287238425156988, 0.7362022492314204}, 0.021747623258421556], InsetBox["3", Offset[{2, 2}, {1.5504714657741203, 0.7579498724898419}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{1.8942529161068986, 1.6301526560845176}, 0.021747623258421556], InsetBox["4", Offset[{2, 2}, {1.91600053936532, 1.6519002793429391}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{0., 1.5971067069485696}, 0.021747623258421556], InsetBox["5", Offset[{2, 2}, {0.021747623258421556, 1.618854330206991}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{0.39595435322445827, 0.715215894120093}, 0.021747623258421556], InsetBox["6", Offset[{2, 2}, {0.4177019764828798, 0.7369635173785145}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{0.9444696686534727, 1.6884854862795353}, 0.021747623258421556], InsetBox["7", Offset[{2, 2}, {0.9662172919118943, 1.7102331095379568}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}}}], MouseAppearanceTag["NetworkGraphics"]], AllowKernelInitialization->False]], DefaultBaseStyle->{ "NetworkGraphics", FrontEnd`GraphicsHighlightColor -> Hue[0.8, 1., 0.6]}, FormatType->TraditionalForm, FrameTicks->None]], "Output", CellChangeTimes->{3.832152349483034*^9}, CellLabel->"Out[20]=",ExpressionUUID->"641e773a-b500-4f27-81a6-4d782b7e80a5"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"IGFaces", "[", "adjv7f81g", "]"}]], "Input", CellChangeTimes->{{3.8321520464064884`*^9, 3.832152058450184*^9}, { 3.832154289788722*^9, 3.8321542922136545`*^9}},ExpressionUUID->"83a39468-708b-41f1-b957-\ dad017b790e9"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "2", ",", "3", ",", "4"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "4", ",", "7"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "7", ",", "5"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "5", ",", "6", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "6", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"3", ",", "6", ",", "7"}], "}"}], ",", RowBox[{"{", RowBox[{"3", ",", "7", ",", "4"}], "}"}], ",", RowBox[{"{", RowBox[{"5", ",", "7", ",", "6"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.832152059399657*^9}, CellLabel->"Out[18]=",ExpressionUUID->"710aca9d-8697-4e23-a5e0-c7777893aaab"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"IGDualGraph", "[", RowBox[{"adjv7f81g", ",", RowBox[{"VertexLabels", "\[Rule]", "\"\\""}]}], "]"}]], "Input", CellChangeTimes->{{3.832152061299717*^9, 3.8321520747444305`*^9}}, CellLabel->"In[19]:=",ExpressionUUID->"4b9f2dab-46a2-4aa7-aa04-5e36e95a7fd6"], Cell[BoxData[ GraphicsBox[ NamespaceBox["NetworkGraphics", DynamicModuleBox[{Typeset`graph = HoldComplete[ Graph[{1, 2, 3, 4, 5, 6, 7, 8}, { Null, {{1, 4}, {2, 1}, {4, 3}, {3, 2}, {1, 5}, {5, 4}, {1, 7}, {6, 5}, { 7, 6}, {2, 7}, {4, 8}, {8, 3}, {6, 8}}}, {VertexLabels -> {"Name"}}]]}, TagBox[GraphicsGroupBox[{ {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[0.], ArrowBox[CompressedData[" 1:eJxTTMoPSmVmYGDgBWImKD7CfHr29oif9m+vzzXfMvWZ/RrxREMhsW/2DFCA Lj+hvCD376Fn9nwpXRYbVn6wR5df9d5uuZ7QT/uaHK5DjR9+Ych7iEcnbLNk cMiquc9XvOYDhn082+/f0pE7Z8/RaLojNvwKhjy6fnT16O5Dl4eZczXhwPpH cd8w1KO7H10eXT+6er5Oo5sS4R/s31wWK1q96D8GH9396PLo5gMAope6tw== "], 0.022839704630862573`]}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[ 0.7]}], { DiskBox[{1.5841594777741514, 0.7057744108449221}, 0.022839704630862573], InsetBox["1", Offset[{2, 2}, {1.606999182405014, 0.7286141154757847}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{1.3803884438398013, 0.}, 0.022839704630862573], InsetBox["2", Offset[{2, 2}, {1.403228148470664, 0.022839704630862573}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{0.23529587447358613, 0.3178324030796067}, 0.022839704630862573], InsetBox["3", Offset[{2, 2}, {0.25813557910444873, 0.3406721077104693}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{0.7113024842726521, 1.041427822934796}, 0.022839704630862573], InsetBox["4", Offset[{2, 2}, {0.7341421889035147, 1.0642675275656586}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{1.5669390233078766, 1.68371749684482}, 0.022839704630862573], InsetBox["5", Offset[{2, 2}, {1.5897787279387392, 1.7065572014756827}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{1.021263931681975, 1.977214284573388}, 0.022839704630862573], InsetBox["6", Offset[{2, 2}, {1.0441036363128375, 2.0000539892042504}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{2.0281798866080045, 1.0421019154526001}, 0.022839704630862573], InsetBox["7", Offset[{2, 2}, {2.051019591238867, 1.0649416200834627}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{0., 1.398165403870782}, 0.022839704630862573], InsetBox["8", Offset[{2, 2}, {0.022839704630862573, 1.4210051085016446}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}}}], MouseAppearanceTag["NetworkGraphics"]], AllowKernelInitialization->False]], DefaultBaseStyle->{ "NetworkGraphics", FrontEnd`GraphicsHighlightColor -> Hue[0.8, 1., 0.6]}, FormatType->TraditionalForm, FrameTicks->None]], "Output", CellChangeTimes->{3.832152076231894*^9}, CellLabel->"Out[19]=",ExpressionUUID->"63012f7f-d7f8-4ffe-a714-9df424cfad3f"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"adjv7f81dg", "=", RowBox[{"PlanarGraph", "[", RowBox[{"IGDualGraph", "[", RowBox[{"adjv7f81g", ",", RowBox[{"VertexLabels", "\[Rule]", "\"\\""}]}], "]"}], "]"}]}]], "Input", CellChangeTimes->{{3.832151965089308*^9, 3.832151992188071*^9}, 3.8321520235899696`*^9, {3.8321526522557116`*^9, 3.8321526648433747`*^9}}, CellLabel->"In[21]:=",ExpressionUUID->"235f890e-1865-4497-964b-8145d5c9f184"], Cell[BoxData[ GraphicsBox[ NamespaceBox["NetworkGraphics", DynamicModuleBox[{Typeset`graph = HoldComplete[ Graph[{1, 2, 3, 4, 5, 6, 7, 8}, { Null, {{1, 4}, {2, 1}, {4, 3}, {3, 2}, {1, 5}, {5, 4}, {1, 7}, {6, 5}, { 7, 6}, {2, 7}, {4, 8}, {8, 3}, {6, 8}}}, { GraphLayout -> "TutteEmbedding", VertexLabels -> {"Name"}}]]}, TagBox[GraphicsGroupBox[{ {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[0.], ArrowBox[CompressedData[" 1:eJxTTMoPSmVmYGDgBWImKL7z+6GnWP2p/e+X+Thv6D1nz9U1z8eyctUeBjD4 YI8uv2lu8OqI+ZfstWecPvGzef9+dPmfvBsYf9cd3f92eW0U37SzGPIMoS7C fPnv9nu/1Dd/f+wyhn3/Q8Dy9oE45NH1o6tHdx+6fFxUKYvy+Uf2y79Mn13+ +OV+dPXo7keXR9ePrj4WIr9/JVQenY/ufnR5dPMB9ODdjQ== "], 0.021812234931106983`]}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[ 0.7]}], { DiskBox[{-0.20700338943058127, 0.23869899068932152}, 0.021812234931106983], InsetBox["1", Offset[{2, 2}, {-0.1851911544994743, 0.2605112256204285}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{-1.8369701987210297*^-16, 1.}, 0.021812234931106983], InsetBox["2", Offset[{2, 2}, {0.0218122349311068, 1.021812234931107}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{0.9510565162951535, 0.3090169943749475}, 0.021812234931106983], InsetBox["3", Offset[{2, 2}, {0.9728687512262605, 0.3308292293060545}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{0.2909757302390644, -0.12310753967503334}, 0.021812234931106983], InsetBox["4", Offset[{2, 2}, {0.3127879651701714, -0.10129530474392635}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{-0.16793763716132995, -0.23114184778688643}, 0.021812234931106983], InsetBox["5", Offset[{2, 2}, {-0.14612540223022297, -0.20932961285577945}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{-0.587785252292473, -0.8090169943749476}, 0.021812234931106983], InsetBox["6", Offset[{2, 2}, {-0.5659730173613661, -0.7872047594438406}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{-0.9510565162951536, 0.3090169943749472}, 0.021812234931106983], InsetBox["7", Offset[{2, 2}, {-0.9292442813640467, 0.3308292293060542}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{0.5877852522924731, -0.8090169943749473}, 0.021812234931106983], InsetBox["8", Offset[{2, 2}, {0.6095974872235801, -0.7872047594438404}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}}}], MouseAppearanceTag["NetworkGraphics"]], AllowKernelInitialization->False]], DefaultBaseStyle->{ "NetworkGraphics", FrontEnd`GraphicsHighlightColor -> Hue[0.8, 1., 0.6]}, FormatType->TraditionalForm, FrameTicks->None]], "Output", CellChangeTimes->{3.8321520296971292`*^9, 3.8321526672921405`*^9}, CellLabel->"Out[21]=",ExpressionUUID->"3a94e9ac-7446-490c-a487-d9b2bf17b1d0"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"IGFaces", "[", "adjv7f81dg", "]"}]], "Input", CellChangeTimes->{{3.832153175562317*^9, 3.832153182358927*^9}}, CellLabel->"In[25]:=",ExpressionUUID->"f44092de-6097-4af2-99ed-6d23bbb72a2b"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "4", ",", "5"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "5", ",", "6", ",", "7"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "7", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "2", ",", "3", ",", "4"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "7", ",", "6", ",", "8", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"3", ",", "8", ",", "4"}], "}"}], ",", RowBox[{"{", RowBox[{"4", ",", "8", ",", "6", ",", "5"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.832153183401061*^9}, CellLabel->"Out[25]=",ExpressionUUID->"55668a9a-feb0-4779-8a48-c539fb5e9ac5"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"adjv7f81d", "=", RowBox[{"Normal", "[", RowBox[{"AdjacencyMatrix", "[", "adjv7f81dg", "]"}], "]"}]}]], "Input", CellChangeTimes->{{3.8321526685777006`*^9, 3.83215270881654*^9}, { 3.8321538506936035`*^9, 3.8321538532105985`*^9}}, CellLabel->"In[30]:=",ExpressionUUID->"2a7953b4-0b59-426a-ac32-0c3bd9b6ec1a"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "0", ",", "1", ",", "0", ",", "1", ",", "1", ",", "0", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ "1", ",", "0", ",", "1", ",", "0", ",", "0", ",", "0", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ "0", ",", "1", ",", "0", ",", "1", ",", "0", ",", "0", ",", "0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{ "1", ",", "0", ",", "1", ",", "0", ",", "1", ",", "0", ",", "0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{ "1", ",", "0", ",", "0", ",", "1", ",", "0", ",", "1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ "0", ",", "0", ",", "0", ",", "0", ",", "1", ",", "0", ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{ "1", ",", "1", ",", "0", ",", "0", ",", "0", ",", "1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ "0", ",", "0", ",", "1", ",", "1", ",", "0", ",", "1", ",", "0", ",", "0"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{{3.83215268378087*^9, 3.832152709561654*^9}, 3.8321538539479012`*^9}, CellLabel->"Out[30]=",ExpressionUUID->"7c3b9ca9-f7c7-4e0d-9843-99c485acd962"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"i", "==", "j"}], ",", "1", ",", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"adjv7f81", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "==", "1"}], ",", RowBox[{"-", "1"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"i", ">", "j"}], ",", SubscriptBox["b", RowBox[{"j", ",", "i"}]], ",", SubscriptBox["b", RowBox[{"i", ",", "j"}]], ","}], "]"}]}], "]"}]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", RowBox[{"VertexCount", "[", "adjv7f81g", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", RowBox[{"VertexCount", "[", "adjv7f81g", "]"}]}], "}"}]}], "]"}], "//", "MatrixForm"}]], "Input", CellChangeTimes->{{3.8321536193975573`*^9, 3.8321536594566097`*^9}}, CellLabel->"In[27]:=",ExpressionUUID->"33720663-c33a-4ba7-9741-b7744a5d0c22"], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"1", ",", "3"}]], RowBox[{"-", "1"}], RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"1", ",", "6"}]], RowBox[{"-", "1"}]}, { RowBox[{"-", "1"}], "1", RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"2", ",", "4"}]], SubscriptBox["b", RowBox[{"2", ",", "5"}]], RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"2", ",", "7"}]]}, { SubscriptBox["b", RowBox[{"1", ",", "3"}]], RowBox[{"-", "1"}], "1", RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"3", ",", "5"}]], RowBox[{"-", "1"}], RowBox[{"-", "1"}]}, { RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"2", ",", "4"}]], RowBox[{"-", "1"}], "1", SubscriptBox["b", RowBox[{"4", ",", "5"}]], SubscriptBox["b", RowBox[{"4", ",", "6"}]], RowBox[{"-", "1"}]}, { RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"2", ",", "5"}]], SubscriptBox["b", RowBox[{"3", ",", "5"}]], SubscriptBox["b", RowBox[{"4", ",", "5"}]], "1", RowBox[{"-", "1"}], RowBox[{"-", "1"}]}, { SubscriptBox["b", RowBox[{"1", ",", "6"}]], RowBox[{"-", "1"}], RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"4", ",", "6"}]], RowBox[{"-", "1"}], "1", RowBox[{"-", "1"}]}, { RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"2", ",", "7"}]], RowBox[{"-", "1"}], RowBox[{"-", "1"}], RowBox[{"-", "1"}], RowBox[{"-", "1"}], "1"} }, GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{3.8321536063844495`*^9, 3.8321536613997583`*^9}, CellLabel-> "Out[27]//MatrixForm=",ExpressionUUID->"71a29eb7-bed5-495b-9db8-\ b2077f35b60f"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"i", "==", "j"}], ",", "1", ",", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"adjv7f81d", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "==", "1"}], ",", RowBox[{"-", "1"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"i", ">", "j"}], ",", SubscriptBox["b", RowBox[{ RowBox[{"j", "+", RowBox[{"VertexCount", "[", "adjv7f81g", "]"}]}], ",", RowBox[{"i", "+", RowBox[{"VertexCount", "[", "adjv7f81g", "]"}]}]}]], ",", SubscriptBox["b", RowBox[{ RowBox[{"i", "+", RowBox[{"VertexCount", "[", "adjv7f81g", "]"}]}], ",", RowBox[{"j", "+", RowBox[{"VertexCount", "[", "adjv7f81g", "]"}]}]}]], ","}], "]"}]}], "]"}]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", RowBox[{"VertexCount", "[", "adjv7f81dg", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", RowBox[{"VertexCount", "[", "adjv7f81dg", "]"}]}], "}"}]}], "]"}], "//", "MatrixForm"}]], "Input", CellChangeTimes->{{3.832153673637809*^9, 3.8321537130748577`*^9}, { 3.8321537590245676`*^9, 3.832153814207903*^9}}, CellLabel->"In[51]:=",ExpressionUUID->"bfcff686-9ece-4348-94fc-ffb368c6efc4"], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"8", ",", "10"}]], RowBox[{"-", "1"}], RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"8", ",", "13"}]], RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"8", ",", "15"}]]}, { RowBox[{"-", "1"}], "1", RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"9", ",", "11"}]], SubscriptBox["b", RowBox[{"9", ",", "12"}]], SubscriptBox["b", RowBox[{"9", ",", "13"}]], RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"9", ",", "15"}]]}, { SubscriptBox["b", RowBox[{"8", ",", "10"}]], RowBox[{"-", "1"}], "1", RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"10", ",", "12"}]], SubscriptBox["b", RowBox[{"10", ",", "13"}]], SubscriptBox["b", RowBox[{"10", ",", "14"}]], RowBox[{"-", "1"}]}, { RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"9", ",", "11"}]], RowBox[{"-", "1"}], "1", RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"11", ",", "13"}]], SubscriptBox["b", RowBox[{"11", ",", "14"}]], RowBox[{"-", "1"}]}, { RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"9", ",", "12"}]], SubscriptBox["b", RowBox[{"10", ",", "12"}]], RowBox[{"-", "1"}], "1", RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"12", ",", "14"}]], SubscriptBox["b", RowBox[{"12", ",", "15"}]]}, { SubscriptBox["b", RowBox[{"8", ",", "13"}]], SubscriptBox["b", RowBox[{"9", ",", "13"}]], SubscriptBox["b", RowBox[{"10", ",", "13"}]], SubscriptBox["b", RowBox[{"11", ",", "13"}]], RowBox[{"-", "1"}], "1", RowBox[{"-", "1"}], RowBox[{"-", "1"}]}, { RowBox[{"-", "1"}], RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"10", ",", "14"}]], SubscriptBox["b", RowBox[{"11", ",", "14"}]], SubscriptBox["b", RowBox[{"12", ",", "14"}]], RowBox[{"-", "1"}], "1", SubscriptBox["b", RowBox[{"14", ",", "15"}]]}, { SubscriptBox["b", RowBox[{"8", ",", "15"}]], SubscriptBox["b", RowBox[{"9", ",", "15"}]], RowBox[{"-", "1"}], RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"12", ",", "15"}]], RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"14", ",", "15"}]], "1"} }, GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{3.8321538181044245`*^9, 3.8321538567022066`*^9, 3.8321556314159956`*^9}, CellLabel-> "Out[51]//MatrixForm=",ExpressionUUID->"025b611e-a832-43d2-9ba4-\ c67dcfe46051"] }, Open ]], Cell[BoxData[ RowBox[{"Clear", "[", "i", "]"}]], "Input", CellChangeTimes->{{3.8321561163671446`*^9, 3.8321561173449173`*^9}}, CellLabel->"In[56]:=",ExpressionUUID->"820fe646-2667-40c4-a849-7b960ef3cdd4"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"MemberQ", "[", RowBox[{ RowBox[{ RowBox[{"IGFaces", "[", "adjv7f81g", "]"}], "[", RowBox[{"[", "j", "]"}], "]"}], ",", "i"}], "]"}], ",", "0", ",", SubscriptBox["b", RowBox[{ RowBox[{"j", "+", RowBox[{"VertexCount", "[", "adjv7f81g", "]"}]}], ",", "i"}]]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{"VertexCount", "[", "adjv7f81g", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", RowBox[{"VertexCount", "[", "adjv7f81dg", "]"}]}], "}"}]}], "]"}], "//", "MatrixForm"}]], "Input", CellChangeTimes->{{3.8321538719758396`*^9, 3.832153904109536*^9}, { 3.832153992046734*^9, 3.8321540971196327`*^9}, {3.8321542002048283`*^9, 3.8321542613863535`*^9}, 3.832154305481922*^9, {3.8321550958157854`*^9, 3.8321550989935703`*^9}, {3.8321551353811007`*^9, 3.8321551539831667`*^9}, {3.83215542509334*^9, 3.832155483689664*^9}, { 3.8321556193585663`*^9, 3.83215564429245*^9}, {3.8321560601089478`*^9, 3.8321560610325108`*^9}, {3.832156129265682*^9, 3.8321561774877467`*^9}}, CellLabel->"In[63]:=",ExpressionUUID->"425ee63d-b0e7-4a0a-b27f-dc2e62d286e4"], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"0", "0", "0", "0", SubscriptBox["b", RowBox[{"12", ",", "1"}]], SubscriptBox["b", RowBox[{"13", ",", "1"}]], SubscriptBox["b", RowBox[{"14", ",", "1"}]], SubscriptBox["b", RowBox[{"15", ",", "1"}]]}, {"0", SubscriptBox["b", RowBox[{"9", ",", "2"}]], SubscriptBox["b", RowBox[{"10", ",", "2"}]], "0", "0", SubscriptBox["b", RowBox[{"13", ",", "2"}]], SubscriptBox["b", RowBox[{"14", ",", "2"}]], SubscriptBox["b", RowBox[{"15", ",", "2"}]]}, {"0", SubscriptBox["b", RowBox[{"9", ",", "3"}]], SubscriptBox["b", RowBox[{"10", ",", "3"}]], SubscriptBox["b", RowBox[{"11", ",", "3"}]], "0", "0", "0", SubscriptBox["b", RowBox[{"15", ",", "3"}]]}, {"0", "0", SubscriptBox["b", RowBox[{"10", ",", "4"}]], SubscriptBox["b", RowBox[{"11", ",", "4"}]], SubscriptBox["b", RowBox[{"12", ",", "4"}]], SubscriptBox["b", RowBox[{"13", ",", "4"}]], "0", SubscriptBox["b", RowBox[{"15", ",", "4"}]]}, { SubscriptBox["b", RowBox[{"8", ",", "5"}]], SubscriptBox["b", RowBox[{"9", ",", "5"}]], "0", "0", SubscriptBox["b", RowBox[{"12", ",", "5"}]], SubscriptBox["b", RowBox[{"13", ",", "5"}]], SubscriptBox["b", RowBox[{"14", ",", "5"}]], "0"}, { SubscriptBox["b", RowBox[{"8", ",", "6"}]], SubscriptBox["b", RowBox[{"9", ",", "6"}]], SubscriptBox["b", RowBox[{"10", ",", "6"}]], "0", "0", "0", SubscriptBox["b", RowBox[{"14", ",", "6"}]], "0"}, { SubscriptBox["b", RowBox[{"8", ",", "7"}]], "0", "0", SubscriptBox["b", RowBox[{"11", ",", "7"}]], SubscriptBox["b", RowBox[{"12", ",", "7"}]], "0", "0", "0"} }, GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{{3.8321550903641376`*^9, 3.8321550998230143`*^9}, 3.8321551562466235`*^9, 3.8321554860302477`*^9, 3.8321555788562403`*^9, 3.832156062429685*^9, {3.8321561202448587`*^9, 3.8321561509155483`*^9}, 3.8321561823308973`*^9}, CellLabel-> "Out[63]//MatrixForm=",ExpressionUUID->"79c9a428-9424-41eb-83d3-\ 5eb405674d28"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"MemberQ", "[", RowBox[{ RowBox[{ RowBox[{"IGFaces", "[", "adjv7f81g", "]"}], "[", RowBox[{"[", "j", "]"}], "]"}], ",", "i"}], "]"}], ",", "0", ",", RowBox[{"If", "[", RowBox[{ RowBox[{"i", ">", "j"}], ",", SubscriptBox["b", RowBox[{ RowBox[{"i", "+", RowBox[{"VertexCount", "[", "adjv7f81g", "]"}]}], ",", "j"}]], ",", SubscriptBox["b", RowBox[{ RowBox[{"i", "+", RowBox[{"VertexCount", "[", "adjv7f81g", "]"}]}], ",", "j"}]]}], "]"}]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", RowBox[{"VertexCount", "[", "adjv7f81g", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", RowBox[{"VertexCount", "[", "adjv7f81dg", "]"}]}], "}"}]}], "]"}], "//", "MatrixForm"}]], "Input", CellChangeTimes->{{3.8321556710598536`*^9, 3.832155672168065*^9}, { 3.8321560333856087`*^9, 3.83215603823637*^9}}, CellLabel->"In[54]:=",ExpressionUUID->"ff5021b1-4c20-41c1-b31f-a570510422e1"], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"0", "0", "0", "0", SubscriptBox["b", RowBox[{"8", ",", "5"}]], SubscriptBox["b", RowBox[{"8", ",", "6"}]], SubscriptBox["b", RowBox[{"8", ",", "7"}]], SubscriptBox["b", RowBox[{"8", ",", "8"}]]}, {"0", SubscriptBox["b", RowBox[{"9", ",", "2"}]], SubscriptBox["b", RowBox[{"9", ",", "3"}]], "0", "0", SubscriptBox["b", RowBox[{"9", ",", "6"}]], SubscriptBox["b", RowBox[{"9", ",", "7"}]], SubscriptBox["b", RowBox[{"9", ",", "8"}]]}, {"0", SubscriptBox["b", RowBox[{"10", ",", "2"}]], SubscriptBox["b", RowBox[{"10", ",", "3"}]], SubscriptBox["b", RowBox[{"10", ",", "4"}]], "0", "0", "0", SubscriptBox["b", RowBox[{"10", ",", "8"}]]}, {"0", "0", SubscriptBox["b", RowBox[{"11", ",", "3"}]], SubscriptBox["b", RowBox[{"11", ",", "4"}]], SubscriptBox["b", RowBox[{"11", ",", "5"}]], SubscriptBox["b", RowBox[{"11", ",", "6"}]], "0", SubscriptBox["b", RowBox[{"11", ",", "8"}]]}, { SubscriptBox["b", RowBox[{"12", ",", "1"}]], SubscriptBox["b", RowBox[{"12", ",", "2"}]], "0", "0", SubscriptBox["b", RowBox[{"12", ",", "5"}]], SubscriptBox["b", RowBox[{"12", ",", "6"}]], SubscriptBox["b", RowBox[{"12", ",", "7"}]], "0"}, { SubscriptBox["b", RowBox[{"13", ",", "1"}]], SubscriptBox["b", RowBox[{"13", ",", "2"}]], SubscriptBox["b", RowBox[{"13", ",", "3"}]], "0", "0", "0", SubscriptBox["b", RowBox[{"13", ",", "7"}]], "0"}, { SubscriptBox["b", RowBox[{"14", ",", "1"}]], "0", "0", SubscriptBox["b", RowBox[{"14", ",", "4"}]], SubscriptBox["b", RowBox[{"14", ",", "5"}]], "0", "0", "0"} }, GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{{3.8321556674530945`*^9, 3.8321556730804806`*^9}, 3.832156040322754*^9}, CellLabel-> "Out[54]//MatrixForm=",ExpressionUUID->"8577bd27-7ac3-485c-bfea-\ 50d391429981"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"ArrayFlatten", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"i", "==", "j"}], ",", "1", ",", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"adjv7f81", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "==", "1"}], ",", RowBox[{"-", "1"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"i", ">", "j"}], ",", SubscriptBox["b", RowBox[{"j", ",", "i"}]], ",", SubscriptBox["b", RowBox[{"i", ",", "j"}]]}], "]"}]}], "]"}]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", RowBox[{"VertexCount", "[", "adjv7f81g", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", RowBox[{"VertexCount", "[", "adjv7f81g", "]"}]}], "}"}]}], "]"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"MemberQ", "[", RowBox[{ RowBox[{ RowBox[{"IGFaces", "[", "adjv7f81g", "]"}], "[", RowBox[{"[", "j", "]"}], "]"}], ",", "i"}], "]"}], ",", "0", ",", SubscriptBox["b", RowBox[{ RowBox[{"j", "+", RowBox[{"VertexCount", "[", "adjv7f81g", "]"}]}], ",", "i"}]]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{"VertexCount", "[", "adjv7f81g", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", RowBox[{"VertexCount", "[", "adjv7f81dg", "]"}]}], "}"}]}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"Transpose", "[", RowBox[{"Table", "[", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"MemberQ", "[", RowBox[{ RowBox[{ RowBox[{"IGFaces", "[", "adjv7f81g", "]"}], "[", RowBox[{"[", "j", "]"}], "]"}], ",", "i"}], "]"}], ",", "0", ",", SubscriptBox["b", RowBox[{ RowBox[{"j", "+", RowBox[{"VertexCount", "[", "adjv7f81g", "]"}]}], ",", "i"}]]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{"VertexCount", "[", "adjv7f81g", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", RowBox[{"VertexCount", "[", "adjv7f81dg", "]"}]}], "}"}]}], "]"}], "]"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"i", "==", "j"}], ",", "1", ",", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"adjv7f81d", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "==", "1"}], ",", RowBox[{"-", "1"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"i", ">", "j"}], ",", SubscriptBox["b", RowBox[{ RowBox[{"j", "+", RowBox[{"VertexCount", "[", "adjv7f81g", "]"}]}], ",", RowBox[{"i", "+", RowBox[{"VertexCount", "[", "adjv7f81g", "]"}]}]}]], ",", SubscriptBox["b", RowBox[{ RowBox[{"i", "+", RowBox[{"VertexCount", "[", "adjv7f81g", "]"}]}], ",", RowBox[{"j", "+", RowBox[{"VertexCount", "[", "adjv7f81g", "]"}]}]}]]}], "]"}]}], "]"}]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", RowBox[{"VertexCount", "[", "adjv7f81dg", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", RowBox[{"VertexCount", "[", "adjv7f81dg", "]"}]}], "}"}]}], "]"}]}], "}"}]}], "}"}], "]"}], "//", "MatrixForm"}]], "Input", CellChangeTimes->{{3.8321551796441517`*^9, 3.832155266119403*^9}, { 3.8321562238698173`*^9, 3.8321562510817966`*^9}, {3.832156901692502*^9, 3.8321569293394103`*^9}, {3.8321569996880407`*^9, 3.832157003175684*^9}}, CellLabel->"In[74]:=",ExpressionUUID->"8b24820b-d092-4777-b98a-ae695521c9c2"], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"1", ",", "3"}]], RowBox[{"-", "1"}], RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"1", ",", "6"}]], RowBox[{"-", "1"}], "0", "0", "0", "0", SubscriptBox["b", RowBox[{"12", ",", "1"}]], SubscriptBox["b", RowBox[{"13", ",", "1"}]], SubscriptBox["b", RowBox[{"14", ",", "1"}]], SubscriptBox["b", RowBox[{"15", ",", "1"}]]}, { RowBox[{"-", "1"}], "1", RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"2", ",", "4"}]], SubscriptBox["b", RowBox[{"2", ",", "5"}]], RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"2", ",", "7"}]], "0", SubscriptBox["b", RowBox[{"9", ",", "2"}]], SubscriptBox["b", RowBox[{"10", ",", "2"}]], "0", "0", SubscriptBox["b", RowBox[{"13", ",", "2"}]], SubscriptBox["b", RowBox[{"14", ",", "2"}]], SubscriptBox["b", RowBox[{"15", ",", "2"}]]}, { SubscriptBox["b", RowBox[{"1", ",", "3"}]], RowBox[{"-", "1"}], "1", RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"3", ",", "5"}]], RowBox[{"-", "1"}], RowBox[{"-", "1"}], "0", SubscriptBox["b", RowBox[{"9", ",", "3"}]], SubscriptBox["b", RowBox[{"10", ",", "3"}]], SubscriptBox["b", RowBox[{"11", ",", "3"}]], "0", "0", "0", SubscriptBox["b", RowBox[{"15", ",", "3"}]]}, { RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"2", ",", "4"}]], RowBox[{"-", "1"}], "1", SubscriptBox["b", RowBox[{"4", ",", "5"}]], SubscriptBox["b", RowBox[{"4", ",", "6"}]], RowBox[{"-", "1"}], "0", "0", SubscriptBox["b", RowBox[{"10", ",", "4"}]], SubscriptBox["b", RowBox[{"11", ",", "4"}]], SubscriptBox["b", RowBox[{"12", ",", "4"}]], SubscriptBox["b", RowBox[{"13", ",", "4"}]], "0", SubscriptBox["b", RowBox[{"15", ",", "4"}]]}, { RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"2", ",", "5"}]], SubscriptBox["b", RowBox[{"3", ",", "5"}]], SubscriptBox["b", RowBox[{"4", ",", "5"}]], "1", RowBox[{"-", "1"}], RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"8", ",", "5"}]], SubscriptBox["b", RowBox[{"9", ",", "5"}]], "0", "0", SubscriptBox["b", RowBox[{"12", ",", "5"}]], SubscriptBox["b", RowBox[{"13", ",", "5"}]], SubscriptBox["b", RowBox[{"14", ",", "5"}]], "0"}, { SubscriptBox["b", RowBox[{"1", ",", "6"}]], RowBox[{"-", "1"}], RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"4", ",", "6"}]], RowBox[{"-", "1"}], "1", RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"8", ",", "6"}]], SubscriptBox["b", RowBox[{"9", ",", "6"}]], SubscriptBox["b", RowBox[{"10", ",", "6"}]], "0", "0", "0", SubscriptBox["b", RowBox[{"14", ",", "6"}]], "0"}, { RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"2", ",", "7"}]], RowBox[{"-", "1"}], RowBox[{"-", "1"}], RowBox[{"-", "1"}], RowBox[{"-", "1"}], "1", SubscriptBox["b", RowBox[{"8", ",", "7"}]], "0", "0", SubscriptBox["b", RowBox[{"11", ",", "7"}]], SubscriptBox["b", RowBox[{"12", ",", "7"}]], "0", "0", "0"}, {"0", "0", "0", "0", SubscriptBox["b", RowBox[{"8", ",", "5"}]], SubscriptBox["b", RowBox[{"8", ",", "6"}]], SubscriptBox["b", RowBox[{"8", ",", "7"}]], "1", RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"8", ",", "10"}]], RowBox[{"-", "1"}], RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"8", ",", "13"}]], RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"8", ",", "15"}]]}, {"0", SubscriptBox["b", RowBox[{"9", ",", "2"}]], SubscriptBox["b", RowBox[{"9", ",", "3"}]], "0", SubscriptBox["b", RowBox[{"9", ",", "5"}]], SubscriptBox["b", RowBox[{"9", ",", "6"}]], "0", RowBox[{"-", "1"}], "1", RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"9", ",", "11"}]], SubscriptBox["b", RowBox[{"9", ",", "12"}]], SubscriptBox["b", RowBox[{"9", ",", "13"}]], RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"9", ",", "15"}]]}, {"0", SubscriptBox["b", RowBox[{"10", ",", "2"}]], SubscriptBox["b", RowBox[{"10", ",", "3"}]], SubscriptBox["b", RowBox[{"10", ",", "4"}]], "0", SubscriptBox["b", RowBox[{"10", ",", "6"}]], "0", SubscriptBox["b", RowBox[{"8", ",", "10"}]], RowBox[{"-", "1"}], "1", RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"10", ",", "12"}]], SubscriptBox["b", RowBox[{"10", ",", "13"}]], SubscriptBox["b", RowBox[{"10", ",", "14"}]], RowBox[{"-", "1"}]}, {"0", "0", SubscriptBox["b", RowBox[{"11", ",", "3"}]], SubscriptBox["b", RowBox[{"11", ",", "4"}]], "0", "0", SubscriptBox["b", RowBox[{"11", ",", "7"}]], RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"9", ",", "11"}]], RowBox[{"-", "1"}], "1", RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"11", ",", "13"}]], SubscriptBox["b", RowBox[{"11", ",", "14"}]], RowBox[{"-", "1"}]}, { SubscriptBox["b", RowBox[{"12", ",", "1"}]], "0", "0", SubscriptBox["b", RowBox[{"12", ",", "4"}]], SubscriptBox["b", RowBox[{"12", ",", "5"}]], "0", SubscriptBox["b", RowBox[{"12", ",", "7"}]], RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"9", ",", "12"}]], SubscriptBox["b", RowBox[{"10", ",", "12"}]], RowBox[{"-", "1"}], "1", RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"12", ",", "14"}]], SubscriptBox["b", RowBox[{"12", ",", "15"}]]}, { SubscriptBox["b", RowBox[{"13", ",", "1"}]], SubscriptBox["b", RowBox[{"13", ",", "2"}]], "0", SubscriptBox["b", RowBox[{"13", ",", "4"}]], SubscriptBox["b", RowBox[{"13", ",", "5"}]], "0", "0", SubscriptBox["b", RowBox[{"8", ",", "13"}]], SubscriptBox["b", RowBox[{"9", ",", "13"}]], SubscriptBox["b", RowBox[{"10", ",", "13"}]], SubscriptBox["b", RowBox[{"11", ",", "13"}]], RowBox[{"-", "1"}], "1", RowBox[{"-", "1"}], RowBox[{"-", "1"}]}, { SubscriptBox["b", RowBox[{"14", ",", "1"}]], SubscriptBox["b", RowBox[{"14", ",", "2"}]], "0", "0", SubscriptBox["b", RowBox[{"14", ",", "5"}]], SubscriptBox["b", RowBox[{"14", ",", "6"}]], "0", RowBox[{"-", "1"}], RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"10", ",", "14"}]], SubscriptBox["b", RowBox[{"11", ",", "14"}]], SubscriptBox["b", RowBox[{"12", ",", "14"}]], RowBox[{"-", "1"}], "1", SubscriptBox["b", RowBox[{"14", ",", "15"}]]}, { SubscriptBox["b", RowBox[{"15", ",", "1"}]], SubscriptBox["b", RowBox[{"15", ",", "2"}]], SubscriptBox["b", RowBox[{"15", ",", "3"}]], SubscriptBox["b", RowBox[{"15", ",", "4"}]], "0", "0", "0", SubscriptBox["b", RowBox[{"8", ",", "15"}]], SubscriptBox["b", RowBox[{"9", ",", "15"}]], RowBox[{"-", "1"}], RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"12", ",", "15"}]], RowBox[{"-", "1"}], SubscriptBox["b", RowBox[{"14", ",", "15"}]], "1"} }, GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{3.832155268850917*^9, 3.8321562540959654`*^9, 3.832157005093977*^9}, CellLabel-> "Out[74]//MatrixForm=",ExpressionUUID->"ae4afda1-188f-48d5-9571-\ 1066496a0172"] }, Open ]], Cell[BoxData[ RowBox[{"Clear", "[", "adjmat", "]"}]], "Input", CellChangeTimes->{{3.832157951389984*^9, 3.832157956820685*^9}}, CellLabel->"In[91]:=",ExpressionUUID->"eddd9fd0-d33e-4575-a386-bd10c33f3fa4"], Cell[BoxData[""], "Input", CellChangeTimes->{{3.8321551158137116`*^9, 3.8321551174791384`*^9}, { 3.8321563593995905`*^9, 3.832156378466247*^9}, {3.83215642085818*^9, 3.832156487557505*^9}, {3.8321571296034155`*^9, 3.8321571320416594`*^9}, 3.832158073671921*^9},ExpressionUUID->"fcbdfb77-f5f4-4812-8582-\ f636f3456278"], Cell[BoxData[""], "Input", CellChangeTimes->{{3.8321580813222833`*^9, 3.832158081348338*^9}},ExpressionUUID->"cfd1e979-8ec3-4258-8f9d-\ e0dfadfe77a5"], Cell[BoxData[ RowBox[{ RowBox[{"pgraph", "[", "adjmat_", "]"}], ":=", RowBox[{"PlanarGraph", "[", RowBox[{"AdjacencyGraph", "[", RowBox[{"adjmat", ",", RowBox[{"VertexLabels", "\[Rule]", "\"\\""}]}], "]"}], "]"}]}]], "Input", CellChangeTimes->{{3.832157015635466*^9, 3.832157026317275*^9}, { 3.8321570768087626`*^9, 3.832157187087782*^9}, {3.832157260817*^9, 3.832157281243805*^9}, {3.83215738072911*^9, 3.832157439845132*^9}, { 3.8321578106356897`*^9, 3.8321578374593196`*^9}, {3.8321581875796967`*^9, 3.832158191258052*^9}}, CellLabel->"In[97]:=",ExpressionUUID->"6e597ece-867a-46de-89e3-081c9d9596ed"], Cell[BoxData[ RowBox[{ RowBox[{"dgraph", "[", "adjmat_", "]"}], ":=", RowBox[{"PlanarGraph", "[", RowBox[{"IGDualGraph", "[", RowBox[{ RowBox[{"pgraph", "[", "adjmat", "]"}], ",", RowBox[{"VertexLabels", "\[Rule]", "\"\\""}]}], "]"}], "]"}]}]], "Input", CellChangeTimes->{{3.832157448820382*^9, 3.832157476669551*^9}, { 3.832157847353641*^9, 3.832157909605048*^9}, {3.83215819890162*^9, 3.832158204194887*^9}}, CellLabel->"In[98]:=",ExpressionUUID->"91b5ce81-f4b1-4cd3-9e24-14b328a2f65c"], Cell[BoxData[ RowBox[{ RowBox[{"dadjmat", "[", "adjmat_", "]"}], ":=", RowBox[{"Normal", "[", RowBox[{"AdjacencyMatrix", "[", RowBox[{"dgraph", "[", "adjmat", "]"}], "]"}], "]"}]}]], "Input", CellChangeTimes->{{3.8321574651675024`*^9, 3.8321575207418165`*^9}, { 3.832157919355533*^9, 3.832157942375414*^9}}, CellLabel->"In[90]:=",ExpressionUUID->"b9295ba9-49a8-4e4c-a009-5f764b3d466d"], Cell[BoxData[""], "Input", CellChangeTimes->{{3.832157564698201*^9, 3.832157567647537*^9}, 3.832157949016788*^9},ExpressionUUID->"2bfe587e-ee34-4971-8fec-\ a026d2c8ae3a"], Cell[BoxData[ RowBox[{ RowBox[{"exGmat", "[", RowBox[{"adjmat_", ",", "adjmatg_", ",", "adjmatd_", ",", "adjmatdg_"}], "]"}], ":=", RowBox[{"ArrayFlatten", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"i", "==", "j"}], ",", "1", ",", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"adjmat", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "==", "1"}], ",", RowBox[{"-", "1"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"i", ">", "j"}], ",", SubscriptBox["b", RowBox[{"j", ",", "i"}]], ",", SubscriptBox["b", RowBox[{"i", ",", "j"}]]}], "]"}]}], "]"}]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", RowBox[{"VertexCount", "[", "adjmatg", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", RowBox[{"VertexCount", "[", "adjmatg", "]"}]}], "}"}]}], "]"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"MemberQ", "[", RowBox[{ RowBox[{ RowBox[{"IGFaces", "[", "adjmatg", "]"}], "[", RowBox[{"[", "j", "]"}], "]"}], ",", "i"}], "]"}], ",", "0", ",", SubscriptBox["b", RowBox[{ RowBox[{"j", "+", RowBox[{"VertexCount", "[", "adjmatg", "]"}]}], ",", "i"}]]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{"VertexCount", "[", "adjmatg", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", RowBox[{"VertexCount", "[", "adjmatdg", "]"}]}], "}"}]}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"Transpose", "[", RowBox[{"Table", "[", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"MemberQ", "[", RowBox[{ RowBox[{ RowBox[{"IGFaces", "[", "adjmatg", "]"}], "[", RowBox[{"[", "j", "]"}], "]"}], ",", "i"}], "]"}], ",", "0", ",", SubscriptBox["b", RowBox[{ RowBox[{"j", "+", RowBox[{"VertexCount", "[", "adjmatg", "]"}]}], ",", "i"}]]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{"VertexCount", "[", "adjmatg", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", RowBox[{"VertexCount", "[", "adjmatdg", "]"}]}], "}"}]}], "]"}], "]"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"i", "==", "j"}], ",", "1", ",", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"adjmatd", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "==", "1"}], ",", RowBox[{"-", "1"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"i", ">", "j"}], ",", SubscriptBox["b", RowBox[{ RowBox[{"j", "+", RowBox[{"VertexCount", "[", "adjmatg", "]"}]}], ",", RowBox[{"i", "+", RowBox[{"VertexCount", "[", "adjmatg", "]"}]}]}]], ",", SubscriptBox["b", RowBox[{ RowBox[{"i", "+", RowBox[{"VertexCount", "[", "adjmatg", "]"}]}], ",", RowBox[{"j", "+", RowBox[{"VertexCount", "[", "adjmatg", "]"}]}]}]]}], "]"}]}], "]"}]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", RowBox[{"VertexCount", "[", "adjmatdg", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", RowBox[{"VertexCount", "[", "adjmatdg", "]"}]}], "}"}]}], "]"}]}], "}"}]}], "}"}], "]"}]}]], "Input", CellChangeTimes->{{3.8321575269876523`*^9, 3.8321576763644238`*^9}, { 3.832159927387419*^9, 3.8321599288063574`*^9}}, CellLabel->"In[85]:=",ExpressionUUID->"299c55ae-115d-4473-8d66-77da8cf9648e"], Cell[BoxData[""], "Input", CellChangeTimes->{{3.832159893936446*^9, 3.832159919205484*^9}, 3.832159950380535*^9},ExpressionUUID->"2cf46402-d937-4583-8360-\ 80d26e690b1c"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"testshape", "=", RowBox[{"Normal", "[", RowBox[{"AdjacencyMatrix", "[", RowBox[{"{", RowBox[{ RowBox[{"1", "\[UndirectedEdge]", "2"}], ",", RowBox[{"1", "\[UndirectedEdge]", "3"}], ",", RowBox[{"1", "\[UndirectedEdge]", "4"}], ",", RowBox[{"1", "\[UndirectedEdge]", "6"}], ",", RowBox[{"2", "\[UndirectedEdge]", "3"}], ",", RowBox[{"2", "\[UndirectedEdge]", "4"}], ",", RowBox[{"2", "\[UndirectedEdge]", "5"}], ",", RowBox[{"3", "\[UndirectedEdge]", "5"}], ",", RowBox[{"3", "\[UndirectedEdge]", "6"}], ",", RowBox[{"4", "\[UndirectedEdge]", "5"}], ",", RowBox[{"4", "\[UndirectedEdge]", "6"}], ",", RowBox[{"5", "\[UndirectedEdge]", "6"}]}], "}"}], "]"}], "]"}]}]], "Input", CellLabel->"In[96]:=",ExpressionUUID->"964d8e52-ab56-438d-b2bd-6783ab996349"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1", ",", "1", ",", "1", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0", ",", "1", ",", "1", ",", "0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1", ",", "0", ",", "0", ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1", ",", "0", ",", "0", ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0", ",", "1", ",", "1", ",", "0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "1", ",", "1", ",", "1", ",", "0"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.8321580772983904`*^9}, CellLabel->"Out[96]=",ExpressionUUID->"c885976d-7a86-45f7-a291-9f890528a337"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"pgraph", "[", "testshape", "]"}], "\[IndentingNewLine]", RowBox[{"dgraph", "[", "testshape", "]"}], "\[IndentingNewLine]", RowBox[{"dadjmat", "[", "testshape", "]"}]}], "Input", CellChangeTimes->{{3.832157989813452*^9, 3.8321580130229187`*^9}}, CellLabel->"In[99]:=",ExpressionUUID->"c6a2aa5d-c5e9-4cb5-9db7-c126dc4464d0"], Cell[BoxData[ GraphicsBox[ NamespaceBox["NetworkGraphics", DynamicModuleBox[{Typeset`graph = HoldComplete[ Graph[{1, 2, 3, 4, 5, 6}, { Null, {{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}, {2, 6}, {3, 5}, { 3, 6}, {4, 5}, {4, 6}, {5, 6}}}, { GraphLayout -> "TutteEmbedding", VertexLabels -> {"Name"}}]]}, TagBox[GraphicsGroupBox[{ {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[0.], ArrowBox[CompressedData[" 1:eJxTTMoPSmVmYGDgAWImKObqmudjWblqDwMYfLBf7RPxomrba/vf/0Hg/n50 ee5wnR8rtI/Zs66Q0fk2c6c9uvxKiP79LGD+Awz9fzfxCHdqH9v/wzDl4RWg fnT70M1Hl0c3H12egUFiifzT9XaHnvjPa5t5EsM8dPvR5dH1o9uHrh9dHl0/ unp0eQAbe76Z "], 0.020399597244776385`]}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[ 0.7]}], { DiskBox[{-1.8369701987210297*^-16, 1.}, 0.020399597244776385], InsetBox["1", Offset[{2, 2}, {0.0203995972447762, 1.0203995972447764}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{0.8660254037844387, -0.4999999999999997}, 0.020399597244776385], InsetBox["2", Offset[{2, 2}, {0.8864250010292151, -0.4796004027552233}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{0.1732073985846728, 0.10000551773978834}, 0.020399597244776385], InsetBox["3", Offset[{2, 2}, {0.19360699582944918, 0.12040511498456473}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{-0.8660254037844385, -0.5000000000000004}, 0.020399597244776385], InsetBox["4", Offset[{2, 2}, {-0.8456258065396621, -0.4796004027552241}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{-0.17320359640270758, 0.1000035333892767}, 0.020399597244776385], InsetBox["5", Offset[{2, 2}, {-0.1528039991579312, 0.12040313063405308}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{9.505454913738554*^-7, -0.19999773721773378}, 0.020399597244776385], InsetBox["6", Offset[{2, 2}, {0.02040054779026776, -0.1795981399729574}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}}}], MouseAppearanceTag["NetworkGraphics"]], AllowKernelInitialization->False]], DefaultBaseStyle->{ "NetworkGraphics", FrontEnd`GraphicsHighlightColor -> Hue[0.8, 1., 0.6]}, FormatType->TraditionalForm, FrameTicks->None]], "Output", CellChangeTimes->{3.8321580148871107`*^9, 3.8321582135780177`*^9}, CellLabel->"Out[99]=",ExpressionUUID->"66acac4f-7ee3-4dc2-a084-d6afeae61565"], Cell[BoxData[ GraphicsBox[ NamespaceBox["NetworkGraphics", DynamicModuleBox[{Typeset`graph = HoldComplete[ Graph[{1, 2, 3, 4, 5, 6, 7, 8}, { Null, {{1, 4}, {4, 3}, {2, 1}, {3, 2}, {5, 4}, {1, 6}, {6, 5}, {7, 3}, { 5, 7}, {2, 8}, {8, 6}, {7, 8}}}, { GraphLayout -> "TutteEmbedding", VertexLabels -> {"Name"}}]]}, TagBox[GraphicsGroupBox[{ {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[0.], ArrowBox[CompressedData[" 1:eJxTTMoPSmVmYGDgAWImKObqmudjWblqDwMYfLCH0ewxIsZqyxbaoMuHhv66 9jj1qd3/TFbnztCr9jj074fo37gH3TyYvvLNJ44sbHxvhy4PoSfawMxBV49u P7p8+Wb32c8E7tppzggUMAq9uh9dPUx8tRZEHJ2P7n50eXTz0dWjux9dPbo8 AF0blp0= "], 0.02261146496815286]}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[ 0.7]}], {DiskBox[{-1.8369701987210297*^-16, 1.}, 0.02261146496815286], InsetBox["1", Offset[{2, 2}, {0.022611464968152677, 1.0226114649681528}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{1., 1.2246467991473532*^-16}, 0.02261146496815286], InsetBox["2", Offset[{2, 2}, {1.0226114649681528, 0.022611464968152983}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{0.3333457140448956, 0.000015023410150660891}, 0.02261146496815286], InsetBox["3", Offset[{2, 2}, {0.35595717901304846, 0.02262648837830352}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{0.000010203365234754772, 0.3333457140448956}, 0.02261146496815286], InsetBox["4", Offset[{2, 2}, {0.022621668333387617, 0.35595717901304846}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{-0.3333249244082049, 0.00001020336523473627}, 0.02261146496815286], InsetBox["5", Offset[{2, 2}, {-0.310713459440052, 0.022621668333387596}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{-1., -2.4492935982947064*^-16}, 0.02261146496815286], InsetBox["6", Offset[{2, 2}, {-0.9773885350318472, 0.022611464968152615}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{6.929878896927479*^-6, -0.3333249244082049}, 0.02261146496815286], InsetBox["7", Offset[{2, 2}, {0.022618394847049788, -0.310713459440052}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}, { DiskBox[{6.123233995736766*^-17, -1.}, 0.02261146496815286], InsetBox["8", Offset[{2, 2}, {0.022611464968152924, -0.9773885350318472}], ImageScaled[{0, 0}], BaseStyle->"Graphics"]}}}], MouseAppearanceTag["NetworkGraphics"]], AllowKernelInitialization->False]], DefaultBaseStyle->{ "NetworkGraphics", FrontEnd`GraphicsHighlightColor -> Hue[0.8, 1., 0.6]}, FormatType->TraditionalForm, FrameTicks->None]], "Output", CellChangeTimes->{3.8321580148871107`*^9, 3.832158213651153*^9}, CellLabel-> "Out[100]=",ExpressionUUID->"ed8871bd-b467-4a68-b828-988d38b0cc98"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "0", ",", "1", ",", "0", ",", "1", ",", "0", ",", "1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ "1", ",", "0", ",", "1", ",", "0", ",", "0", ",", "0", ",", "0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{ "0", ",", "1", ",", "0", ",", "1", ",", "0", ",", "0", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ "1", ",", "0", ",", "1", ",", "0", ",", "1", ",", "0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ "0", ",", "0", ",", "0", ",", "1", ",", "0", ",", "1", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ "1", ",", "0", ",", "0", ",", "0", ",", "1", ",", "0", ",", "0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{ "0", ",", "0", ",", "1", ",", "0", ",", "1", ",", "0", ",", "0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{ "0", ",", "1", ",", "0", ",", "0", ",", "0", ",", "1", ",", "1", ",", "0"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.8321580148871107`*^9, 3.832158213651153*^9}, CellLabel-> "Out[101]=",ExpressionUUID->"c0fe5c89-7a53-4a9b-937c-b9cbadbfbb22"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"exocta", "=", RowBox[{"exGmat", "[", RowBox[{"testshape", ",", RowBox[{"pgraph", "[", "testshape", "]"}], ",", RowBox[{"dadjmat", "[", "testshape", "]"}], ",", RowBox[{"dgraph", "[", "testshape", "]"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.832157686683095*^9, 3.832157714372127*^9}, { 3.832158029688574*^9, 3.8321580546012907`*^9}, {3.83215895818824*^9, 3.8321589598529243`*^9}, {3.832159620432417*^9, 3.8321596263024545`*^9}}, CellLabel-> "In[108]:=",ExpressionUUID->"a2d63e57-4b61-444b-8e40-b8a3c7bd8d9d"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}], ",", SubscriptBox["b", RowBox[{"1", ",", "6"}]], ",", "0", ",", "0", ",", "0", ",", "0", ",", SubscriptBox["b", RowBox[{"11", ",", "1"}]], ",", SubscriptBox["b", RowBox[{"12", ",", "1"}]], ",", SubscriptBox["b", RowBox[{"13", ",", "1"}]], ",", SubscriptBox["b", RowBox[{"14", ",", "1"}]]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1", ",", RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}], ",", SubscriptBox["b", RowBox[{"2", ",", "5"}]], ",", RowBox[{"-", "1"}], ",", "0", ",", SubscriptBox["b", RowBox[{"8", ",", "2"}]], ",", SubscriptBox["b", RowBox[{"9", ",", "2"}]], ",", "0", ",", "0", ",", "0", ",", SubscriptBox["b", RowBox[{"13", ",", "2"}]], ",", SubscriptBox["b", RowBox[{"14", ",", "2"}]]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}], ",", "1", ",", SubscriptBox["b", RowBox[{"3", ",", "4"}]], ",", RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}], ",", SubscriptBox["b", RowBox[{"7", ",", "3"}]], ",", SubscriptBox["b", RowBox[{"8", ",", "3"}]], ",", "0", ",", "0", ",", "0", ",", SubscriptBox["b", RowBox[{"12", ",", "3"}]], ",", "0", ",", SubscriptBox["b", RowBox[{"14", ",", "3"}]]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}], ",", SubscriptBox["b", RowBox[{"3", ",", "4"}]], ",", "1", ",", RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}], ",", "0", ",", "0", ",", SubscriptBox["b", RowBox[{"9", ",", "4"}]], ",", SubscriptBox["b", RowBox[{"10", ",", "4"}]], ",", SubscriptBox["b", RowBox[{"11", ",", "4"}]], ",", "0", ",", SubscriptBox["b", RowBox[{"13", ",", "4"}]], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", SubscriptBox["b", RowBox[{"2", ",", "5"}]], ",", RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}], ",", "1", ",", RowBox[{"-", "1"}], ",", SubscriptBox["b", RowBox[{"7", ",", "5"}]], ",", "0", ",", "0", ",", SubscriptBox["b", RowBox[{"10", ",", "5"}]], ",", SubscriptBox["b", RowBox[{"11", ",", "5"}]], ",", SubscriptBox["b", RowBox[{"12", ",", "5"}]], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ SubscriptBox["b", RowBox[{"1", ",", "6"}]], ",", RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}], ",", "1", ",", SubscriptBox["b", RowBox[{"7", ",", "6"}]], ",", SubscriptBox["b", RowBox[{"8", ",", "6"}]], ",", SubscriptBox["b", RowBox[{"9", ",", "6"}]], ",", SubscriptBox["b", RowBox[{"10", ",", "6"}]], ",", "0", ",", "0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", SubscriptBox["b", RowBox[{"7", ",", "3"}]], ",", "0", ",", SubscriptBox["b", RowBox[{"7", ",", "5"}]], ",", SubscriptBox["b", RowBox[{"7", ",", "6"}]], ",", "1", ",", RowBox[{"-", "1"}], ",", SubscriptBox["b", RowBox[{"7", ",", "9"}]], ",", RowBox[{"-", "1"}], ",", SubscriptBox["b", RowBox[{"7", ",", "11"}]], ",", RowBox[{"-", "1"}], ",", SubscriptBox["b", RowBox[{"7", ",", "13"}]], ",", SubscriptBox["b", RowBox[{"7", ",", "14"}]]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", SubscriptBox["b", RowBox[{"8", ",", "2"}]], ",", SubscriptBox["b", RowBox[{"8", ",", "3"}]], ",", "0", ",", "0", ",", SubscriptBox["b", RowBox[{"8", ",", "6"}]], ",", RowBox[{"-", "1"}], ",", "1", ",", RowBox[{"-", "1"}], ",", SubscriptBox["b", RowBox[{"8", ",", "10"}]], ",", SubscriptBox["b", RowBox[{"8", ",", "11"}]], ",", SubscriptBox["b", RowBox[{"8", ",", "12"}]], ",", SubscriptBox["b", RowBox[{"8", ",", "13"}]], ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", SubscriptBox["b", RowBox[{"9", ",", "2"}]], ",", "0", ",", SubscriptBox["b", RowBox[{"9", ",", "4"}]], ",", "0", ",", SubscriptBox["b", RowBox[{"9", ",", "6"}]], ",", SubscriptBox["b", RowBox[{"7", ",", "9"}]], ",", RowBox[{"-", "1"}], ",", "1", ",", RowBox[{"-", "1"}], ",", SubscriptBox["b", RowBox[{"9", ",", "11"}]], ",", SubscriptBox["b", RowBox[{"9", ",", "12"}]], ",", RowBox[{"-", "1"}], ",", SubscriptBox["b", RowBox[{"9", ",", "14"}]]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0", ",", SubscriptBox["b", RowBox[{"10", ",", "4"}]], ",", SubscriptBox["b", RowBox[{"10", ",", "5"}]], ",", SubscriptBox["b", RowBox[{"10", ",", "6"}]], ",", RowBox[{"-", "1"}], ",", SubscriptBox["b", RowBox[{"8", ",", "10"}]], ",", RowBox[{"-", "1"}], ",", "1", ",", RowBox[{"-", "1"}], ",", SubscriptBox["b", RowBox[{"10", ",", "12"}]], ",", SubscriptBox["b", RowBox[{"10", ",", "13"}]], ",", SubscriptBox["b", RowBox[{"10", ",", "14"}]]}], "}"}], ",", RowBox[{"{", RowBox[{ SubscriptBox["b", RowBox[{"11", ",", "1"}]], ",", "0", ",", "0", ",", SubscriptBox["b", RowBox[{"11", ",", "4"}]], ",", SubscriptBox["b", RowBox[{"11", ",", "5"}]], ",", "0", ",", SubscriptBox["b", RowBox[{"7", ",", "11"}]], ",", SubscriptBox["b", RowBox[{"8", ",", "11"}]], ",", SubscriptBox["b", RowBox[{"9", ",", "11"}]], ",", RowBox[{"-", "1"}], ",", "1", ",", RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}], ",", SubscriptBox["b", RowBox[{"11", ",", "14"}]]}], "}"}], ",", RowBox[{"{", RowBox[{ SubscriptBox["b", RowBox[{"12", ",", "1"}]], ",", "0", ",", SubscriptBox["b", RowBox[{"12", ",", "3"}]], ",", "0", ",", SubscriptBox["b", RowBox[{"12", ",", "5"}]], ",", "0", ",", RowBox[{"-", "1"}], ",", SubscriptBox["b", RowBox[{"8", ",", "12"}]], ",", SubscriptBox["b", RowBox[{"9", ",", "12"}]], ",", SubscriptBox["b", RowBox[{"10", ",", "12"}]], ",", RowBox[{"-", "1"}], ",", "1", ",", SubscriptBox["b", RowBox[{"12", ",", "13"}]], ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{ SubscriptBox["b", RowBox[{"13", ",", "1"}]], ",", SubscriptBox["b", RowBox[{"13", ",", "2"}]], ",", "0", ",", SubscriptBox["b", RowBox[{"13", ",", "4"}]], ",", "0", ",", "0", ",", SubscriptBox["b", RowBox[{"7", ",", "13"}]], ",", SubscriptBox["b", RowBox[{"8", ",", "13"}]], ",", RowBox[{"-", "1"}], ",", SubscriptBox["b", RowBox[{"10", ",", "13"}]], ",", RowBox[{"-", "1"}], ",", SubscriptBox["b", RowBox[{"12", ",", "13"}]], ",", "1", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{ SubscriptBox["b", RowBox[{"14", ",", "1"}]], ",", SubscriptBox["b", RowBox[{"14", ",", "2"}]], ",", SubscriptBox["b", RowBox[{"14", ",", "3"}]], ",", "0", ",", "0", ",", "0", ",", SubscriptBox["b", RowBox[{"7", ",", "14"}]], ",", RowBox[{"-", "1"}], ",", SubscriptBox["b", RowBox[{"9", ",", "14"}]], ",", SubscriptBox["b", RowBox[{"10", ",", "14"}]], ",", SubscriptBox["b", RowBox[{"11", ",", "14"}]], ",", RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}], ",", "1"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{{3.832157709044917*^9, 3.8321577153676624`*^9}, 3.8321580569922943`*^9, 3.8321596278501883`*^9}, CellLabel-> "Out[108]=",ExpressionUUID->"1c005c8c-9ad2-435f-afdb-9d1f136c9b1e"] }, Open ]], Cell[BoxData[""], "Input", CellChangeTimes->{{3.832159877613784*^9, 3.83215988447575*^9}},ExpressionUUID->"78225083-0814-4be0-bcd2-\ 8de2548e967c"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Solve", "[", RowBox[{ RowBox[{ RowBox[{"Minors", "[", RowBox[{"exocta", ",", "5"}], "]"}], "==", "0"}], ",", RowBox[{"DeleteDuplicates", "[", RowBox[{"Cases", "[", RowBox[{"exocta", ",", SubscriptBox["b", RowBox[{"_", ",", "_"}]], ",", "2"}], "]"}], "]"}]}], "]"}]], "Input", CellChangeTimes->{{3.8321596315268593`*^9, 3.8321596516750774`*^9}, { 3.8321596847961016`*^9, 3.832159750359083*^9}, 3.832159822913616*^9}, CellLabel-> "In[112]:=",ExpressionUUID->"44161243-616a-435b-bafa-4d274803eaba"], Cell[BoxData["$Aborted"], "Output", CellChangeTimes->{3.832159757890657*^9, 3.8321599361706753`*^9}, CellLabel-> "Out[112]=",ExpressionUUID->"c4852ffd-e636-4450-878f-5b25ba51d72f"] }, Open ]], Cell[BoxData[""], "Input", CellChangeTimes->{{3.832158984239458*^9, 3.8321589948404365`*^9}},ExpressionUUID->"5e8c0a70-4747-4908-acbd-\ d204ee84a745"], Cell[BoxData[""], "Input", CellChangeTimes->{{3.8321565248778944`*^9, 3.8321566273117824`*^9}, { 3.832156668158657*^9, 3.832156951000999*^9}, {3.8321569830506334`*^9, 3.832156996816613*^9}},ExpressionUUID->"15cae195-3c84-4ce9-a91d-\ 389acf0902ff"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"DeleteDuplicates", "[", RowBox[{"Cases", "[", RowBox[{"exocta", ",", SubscriptBox["b", RowBox[{"_", ",", "_"}]], ",", "2"}], "]"}], "]"}]], "Input", CellChangeTimes->{{3.832159776403322*^9, 3.8321598131422777`*^9}}, CellLabel-> "In[111]:=",ExpressionUUID->"c26c8315-aa45-4d01-a556-c6636b256249"], Cell[BoxData[ RowBox[{"{", RowBox[{ SubscriptBox["b", RowBox[{"1", ",", "6"}]], ",", SubscriptBox["b", RowBox[{"11", ",", "1"}]], ",", SubscriptBox["b", RowBox[{"12", ",", "1"}]], ",", SubscriptBox["b", RowBox[{"13", ",", "1"}]], ",", SubscriptBox["b", RowBox[{"14", ",", "1"}]], ",", SubscriptBox["b", RowBox[{"2", ",", "5"}]], ",", SubscriptBox["b", RowBox[{"8", ",", "2"}]], ",", SubscriptBox["b", RowBox[{"9", ",", "2"}]], ",", SubscriptBox["b", RowBox[{"13", ",", "2"}]], ",", SubscriptBox["b", RowBox[{"14", ",", "2"}]], ",", SubscriptBox["b", RowBox[{"3", ",", "4"}]], ",", SubscriptBox["b", RowBox[{"7", ",", "3"}]], ",", SubscriptBox["b", RowBox[{"8", ",", "3"}]], ",", SubscriptBox["b", RowBox[{"12", ",", "3"}]], ",", SubscriptBox["b", RowBox[{"14", ",", "3"}]], ",", SubscriptBox["b", RowBox[{"9", ",", "4"}]], ",", SubscriptBox["b", RowBox[{"10", ",", "4"}]], ",", SubscriptBox["b", RowBox[{"11", ",", "4"}]], ",", SubscriptBox["b", RowBox[{"13", ",", "4"}]], ",", SubscriptBox["b", RowBox[{"7", ",", "5"}]], ",", SubscriptBox["b", RowBox[{"10", ",", "5"}]], ",", SubscriptBox["b", RowBox[{"11", ",", "5"}]], ",", SubscriptBox["b", RowBox[{"12", ",", "5"}]], ",", SubscriptBox["b", RowBox[{"7", ",", "6"}]], ",", SubscriptBox["b", RowBox[{"8", ",", "6"}]], ",", SubscriptBox["b", RowBox[{"9", ",", "6"}]], ",", SubscriptBox["b", RowBox[{"10", ",", "6"}]], ",", SubscriptBox["b", RowBox[{"7", ",", "9"}]], ",", SubscriptBox["b", RowBox[{"7", ",", "11"}]], ",", SubscriptBox["b", RowBox[{"7", ",", "13"}]], ",", SubscriptBox["b", RowBox[{"7", ",", "14"}]], ",", SubscriptBox["b", RowBox[{"8", ",", "10"}]], ",", SubscriptBox["b", RowBox[{"8", ",", "11"}]], ",", SubscriptBox["b", RowBox[{"8", ",", "12"}]], ",", SubscriptBox["b", RowBox[{"8", ",", "13"}]], ",", SubscriptBox["b", RowBox[{"9", ",", "11"}]], ",", SubscriptBox["b", RowBox[{"9", ",", "12"}]], ",", SubscriptBox["b", RowBox[{"9", ",", "14"}]], ",", SubscriptBox["b", RowBox[{"10", ",", "12"}]], ",", SubscriptBox["b", RowBox[{"10", ",", "13"}]], ",", SubscriptBox["b", RowBox[{"10", ",", "14"}]], ",", SubscriptBox["b", RowBox[{"11", ",", "14"}]], ",", SubscriptBox["b", RowBox[{"12", ",", "13"}]]}], "}"}]], "Output", CellChangeTimes->{3.832159771319087*^9, 3.832159814752757*^9}, CellLabel-> "Out[111]=",ExpressionUUID->"9c14116f-3a1f-4883-b4bf-805728789665"] }, Open ]] }, WindowSize->{960., 538.75}, WindowMargins->{{-4.5, Automatic}, {Automatic, -4.5}}, Magnification:>0.7 Inherited, FrontEndVersion->"12.3 for Microsoft Windows (64-bit) (May 11, 2021)", StyleDefinitions->"Default.nb", ExpressionUUID->"f43322f5-32c5-4543-aac9-72e2638f6624" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[580, 22, 359, 6, 21, "Input",ExpressionUUID->"aff1ddef-8716-4588-a33d-a6327039d59d"], Cell[CellGroupData[{ Cell[964, 32, 408, 10, 17, "Print",ExpressionUUID->"6bc201f1-e6df-4076-bf01-856fe692e727"], Cell[1375, 44, 19196, 356, 55, "Print",ExpressionUUID->"5d32e2af-05fa-4461-8796-9099e2115a5e"], Cell[20574, 402, 1180, 32, 18, "Print",ExpressionUUID->"510e29d7-e907-4147-8d8b-fccc5c0f2dde"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[21803, 440, 198, 3, 21, "Input",ExpressionUUID->"8f83865d-4965-40c5-8bad-4548bbcd09d9"], Cell[22004, 445, 696, 14, 20, "Message",ExpressionUUID->"89d96776-46a4-4a8f-94d2-82872e013c08"], Cell[22703, 461, 538, 11, 38, "Output",ExpressionUUID->"a3a99bb6-9bd7-4e76-a352-31154db4eb73"] }, Open ]], Cell[23256, 475, 211, 3, 21, "Input",ExpressionUUID->"0ea0ed7d-9f23-4291-a21c-09d5c95a9618"], Cell[CellGroupData[{ Cell[23492, 482, 656, 15, 21, "Input",ExpressionUUID->"51e42d7b-5dd8-4cea-ae46-9aa90b09347c"], Cell[24151, 499, 8116, 144, 251, "Output",ExpressionUUID->"280a74ae-016d-433f-ae26-c90945eee3bc"] }, Open ]], Cell[CellGroupData[{ Cell[32304, 648, 322, 6, 21, "Input",ExpressionUUID->"570405f9-cea4-4018-bd71-20995bb7d8e5"], Cell[32629, 656, 2139, 53, 235, "Output",ExpressionUUID->"e3608828-45a9-48a3-82d1-f495941c3684"] }, Open ]], Cell[CellGroupData[{ Cell[34805, 714, 274, 4, 34, "Input",ExpressionUUID->"327e16cd-3ee9-4db6-971c-83ea808b2811"], Cell[35082, 720, 555, 15, 23, "Output",ExpressionUUID->"35f88189-eb85-4dc8-9379-aaea1f17764f"], Cell[35640, 737, 1278, 25, 201, "Output",ExpressionUUID->"0783fc8a-c210-4dee-bf52-f2d394f0efd1"] }, Open ]], Cell[CellGroupData[{ Cell[36955, 767, 380, 8, 21, "Input",ExpressionUUID->"fb51fdc0-b4b8-4e35-a730-47920cc7a454"], Cell[37338, 777, 2509, 50, 267, "Output",ExpressionUUID->"2298d2cc-a87b-459b-92cc-91f57c80e872"] }, Open ]], Cell[CellGroupData[{ Cell[39884, 832, 935, 20, 21, "Input",ExpressionUUID->"fbe79ba7-14a6-45d3-8833-f61300e84e0e"], Cell[40822, 854, 974, 25, 23, "Output",ExpressionUUID->"a79ec2f5-4b2d-4b53-9c75-548d2f881696"] }, Open ]], Cell[CellGroupData[{ Cell[41833, 884, 374, 8, 21, "Input",ExpressionUUID->"77197402-7fe7-49d7-a4df-2184ff05418a"], Cell[42210, 894, 2884, 62, 267, "Output",ExpressionUUID->"b788abdc-4b95-46b8-a744-2c76ccc02d73"] }, Open ]], Cell[CellGroupData[{ Cell[45131, 961, 298, 5, 21, "Input",ExpressionUUID->"b71c9604-f901-4019-a986-e0e35b58486a"], Cell[45432, 968, 3011, 67, 241, "Output",ExpressionUUID->"641e773a-b500-4f27-81a6-4d782b7e80a5"] }, Open ]], Cell[CellGroupData[{ Cell[48480, 1040, 247, 5, 21, "Input",ExpressionUUID->"83a39468-708b-41f1-b957-dad017b790e9"], Cell[48730, 1047, 746, 20, 23, "Output",ExpressionUUID->"710aca9d-8697-4e23-a5e0-c7777893aaab"] }, Open ]], Cell[CellGroupData[{ Cell[49513, 1072, 294, 5, 21, "Input",ExpressionUUID->"4b9f2dab-46a2-4aa7-aa04-5e36e95a7fd6"], Cell[49810, 1079, 3150, 71, 261, "Output",ExpressionUUID->"63012f7f-d7f8-4ffe-a714-9df424cfad3f"] }, Open ]], Cell[CellGroupData[{ Cell[52997, 1155, 449, 9, 21, "Input",ExpressionUUID->"235f890e-1865-4497-964b-8145d5c9f184"], Cell[53449, 1166, 3261, 72, 256, "Output",ExpressionUUID->"3a94e9ac-7446-490c-a487-d9b2bf17b1d0"] }, Open ]], Cell[CellGroupData[{ Cell[56747, 1243, 214, 3, 21, "Input",ExpressionUUID->"f44092de-6097-4af2-99ed-6d23bbb72a2b"], Cell[56964, 1248, 707, 18, 23, "Output",ExpressionUUID->"55668a9a-feb0-4779-8a48-c539fb5e9ac5"] }, Open ]], Cell[CellGroupData[{ Cell[57708, 1271, 341, 6, 21, "Input",ExpressionUUID->"2a7953b4-0b59-426a-ac32-0c3bd9b6ec1a"], Cell[58052, 1279, 1265, 37, 36, "Output",ExpressionUUID->"7c3b9ca9-f7c7-4e0d-9843-99c485acd962"] }, Open ]], Cell[CellGroupData[{ Cell[59354, 1321, 1059, 29, 22, "Input",ExpressionUUID->"33720663-c33a-4ba7-9741-b7744a5d0c22"], Cell[60416, 1352, 2342, 82, 105, "Output",ExpressionUUID->"71a29eb7-bed5-495b-9db8-b2077f35b60f"] }, Open ]], Cell[CellGroupData[{ Cell[62795, 1439, 1481, 39, 37, "Input",ExpressionUUID->"bfcff686-9ece-4348-94fc-ffb368c6efc4"], Cell[64279, 1480, 3253, 112, 119, "Output",ExpressionUUID->"025b611e-a832-43d2-9ba4-c67dcfe46051"] }, Open ]], Cell[67547, 1595, 207, 3, 21, "Input",ExpressionUUID->"820fe646-2667-40c4-a849-7b960ef3cdd4"], Cell[CellGroupData[{ Cell[67779, 1602, 1300, 30, 22, "Input",ExpressionUUID->"425ee63d-b0e7-4a0a-b27f-dc2e62d286e4"], Cell[69082, 1634, 2766, 87, 105, "Output",ExpressionUUID->"79c9a428-9424-41eb-83d3-5eb405674d28"] }, Open ]], Cell[CellGroupData[{ Cell[71885, 1726, 1190, 32, 35, "Input",ExpressionUUID->"ff5021b1-4c20-41c1-b31f-a570510422e1"], Cell[73078, 1760, 2610, 85, 105, "Output",ExpressionUUID->"8577bd27-7ac3-485c-bfea-50d391429981"] }, Open ]], Cell[CellGroupData[{ Cell[75725, 1850, 4544, 118, 83, "Input",ExpressionUUID->"8b24820b-d092-4777-b98a-ae695521c9c2"], Cell[80272, 1970, 8825, 297, 214, "Output",ExpressionUUID->"ae4afda1-188f-48d5-9571-1066496a0172"] }, Open ]], Cell[89112, 2270, 208, 3, 21, "Input",ExpressionUUID->"eddd9fd0-d33e-4575-a386-bd10c33f3fa4"], Cell[89323, 2275, 330, 5, 21, "Input",ExpressionUUID->"fcbdfb77-f5f4-4812-8582-f636f3456278"], Cell[89656, 2282, 154, 3, 21, InheritFromParent,ExpressionUUID->"cfd1e979-8ec3-4258-8f9d-e0dfadfe77a5"], Cell[89813, 2287, 648, 13, 21, "Input",ExpressionUUID->"6e597ece-867a-46de-89e3-081c9d9596ed"], Cell[90464, 2302, 532, 12, 21, "Input",ExpressionUUID->"91b5ce81-f4b1-4cd3-9e24-14b328a2f65c"], Cell[90999, 2316, 404, 8, 21, "Input",ExpressionUUID->"b9295ba9-49a8-4e4c-a009-5f764b3d466d"], Cell[91406, 2326, 175, 3, 21, "Input",ExpressionUUID->"2bfe587e-ee34-4971-8fec-a026d2c8ae3a"], Cell[91584, 2331, 4502, 120, 96, "Input",ExpressionUUID->"299c55ae-115d-4473-8d66-77da8cf9648e"], Cell[96089, 2453, 175, 3, 21, "Input",ExpressionUUID->"2cf46402-d937-4583-8360-80d26e690b1c"], Cell[CellGroupData[{ Cell[96289, 2460, 883, 19, 21, "Input",ExpressionUUID->"964d8e52-ab56-438d-b2bd-6783ab996349"], Cell[97175, 2481, 793, 22, 23, "Output",ExpressionUUID->"c885976d-7a86-45f7-a291-9f890528a337"] }, Open ]], Cell[CellGroupData[{ Cell[98005, 2508, 353, 5, 47, "Input",ExpressionUUID->"c6a2aa5d-c5e9-4cb5-9db7-c126dc4464d0"], Cell[98361, 2515, 2699, 60, 235, "Output",ExpressionUUID->"66acac4f-7ee3-4dc2-a084-d6afeae61565"], Cell[101063, 2577, 3147, 69, 267, "Output",ExpressionUUID->"ed8871bd-b467-4a68-b828-988d38b0cc98"], Cell[104213, 2648, 1242, 37, 36, "Output",ExpressionUUID->"c0fe5c89-7a53-4a9b-937c-b9cbadbfbb22"] }, Open ]], Cell[CellGroupData[{ Cell[105492, 2690, 567, 11, 21, "Input",ExpressionUUID->"a2d63e57-4b61-444b-8e40-b8a3c7bd8d9d"], Cell[106062, 2703, 8317, 255, 92, "Output",ExpressionUUID->"1c005c8c-9ad2-435f-afdb-9d1f136c9b1e"] }, Open ]], Cell[114394, 2961, 151, 3, 21, "Input",ExpressionUUID->"78225083-0814-4be0-bcd2-8de2548e967c"], Cell[CellGroupData[{ Cell[114570, 2968, 572, 14, 22, "Input",ExpressionUUID->"44161243-616a-435b-bafa-4d274803eaba"], Cell[115145, 2984, 184, 3, 23, "Output",ExpressionUUID->"c4852ffd-e636-4450-878f-5b25ba51d72f"] }, Open ]], Cell[115344, 2990, 154, 3, 21, "Input",ExpressionUUID->"5e8c0a70-4747-4908-acbd-d204ee84a745"], Cell[115501, 2995, 253, 4, 21, "Input",ExpressionUUID->"15cae195-3c84-4ce9-a91d-389acf0902ff"], Cell[CellGroupData[{ Cell[115779, 3003, 341, 8, 22, "Input",ExpressionUUID->"c26c8315-aa45-4d01-a556-c6636b256249"], Cell[116123, 3013, 2729, 91, 37, "Output",ExpressionUUID->"9c14116f-3a1f-4883-b4bf-805728789665"] }, Open ]] } ] *)