Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 RegularGraphQ

Source Notebook

Return True if a graph is regular

Contributed by: Alejandra Ortiz Duran

ResourceFunction["RegularGraphQ"][g]

yields True if g is a regular graph, and False otherwise.

ResourceFunction["RegularGraphQ"][g,"In"]

yields True if g is a In-regular graph, and False otherwise.

ResourceFunction["RegularGraphQ"][g,"Out"]

yields True if g is a Out-regular graph, and False otherwise.

ResourceFunction["RegularGraphQ"][g,k]

yields True if g is a k-regular graph, and False otherwise.

ResourceFunction["RegularGraphQ"][g,k,"In"]

yields True if g is a k-In-regular graph, and False otherwise.

ResourceFunction["RegularGraphQ"][g,k,"Out"]

yields True if g is a k-Out-regular graph, and False otherwise.

Details

A regular graph is a graph where each vertex has the same degree or valence.
A regular directed graph is a graph where the indegree and outdegree of all vertices are equal.
A In-regular graph is a graph where the indegree of all vertices are equal.
A Out-regular graph is a graph where the outdegree of all vertices are equal.
ResourceFunction["RegularGraphQ"] works with undirected graphs, directed graphs, multigraphs and mixed graphs.

Examples

Basic Examples (6) 

Test whether a graph is a regular graph:

In[1]:=
ResourceFunction["RegularGraphQ"][\!\(\* GraphicsBox[ NamespaceBox["NetworkGraphics", DynamicModuleBox[{Typeset`graph = HoldComplete[ Graph[{1, 2, 3, 4}, {Null, SparseArray[ Automatic, {4, 4}, 0, {1, {{0, 3, 6, 9, 12}, {{2}, {3}, {4}, {1}, {3}, {4}, { 1}, {2}, {4}, {1}, {2}, {3}}}, Pattern}]}, {GraphLayout -> "StarEmbedding"}]]}, TagBox[GraphicsGroupBox[ GraphicsComplexBox[{{0., 0.}, { 0.8660254037844389, -0.5000000000000012}, { 1.8369701987210297`*^-16, 1.}, {-0.8660254037844386, -0.49999999999999917`}}, { {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[0.], ArrowBox[{{1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}}, 0.020399597244776413`]}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], DiskBox[1, 0.020399597244776413], DiskBox[2, 0.020399597244776413], DiskBox[3, 0.020399597244776413], DiskBox[4, 0.020399597244776413]}}]], MouseAppearanceTag["NetworkGraphics"]], AllowKernelInitialization->False]], DefaultBaseStyle->"NetworkGraphics", FormatType->TraditionalForm, FrameTicks->None, ImageSize->{89.39999999999998, Automatic}]\)]
Out[1]=
In[2]:=
ResourceFunction["RegularGraphQ"][\!\(\* GraphicsBox[ NamespaceBox["NetworkGraphics", DynamicModuleBox[{Typeset`graph = HoldComplete[ Graph[{1, 2, 3, 4}, { SparseArray[ Automatic, {4, 4}, 0, {1, {{0, 2, 4, 7, 10}, {{3}, {4}, {3}, {4}, {1}, {2}, { 4}, {1}, {2}, {3}}}, Pattern}], Null}, {GraphLayout -> {"Dimension" -> 2}, VertexCoordinates -> {{0., 0.}, { 0.8660254037844389, -0.5000000000000012}, { 1.8369701987210297`*^-16, 1.}, {-0.8660254037844386, -0.49999999999999917`}}}]]}, TagBox[GraphicsGroupBox[GraphicsComplexBox[CompressedData[" 1:eJxd1Xs41PkewPFBKwaxslanrdVj0aOEss6Q+qij1UYutSulrEpqJUonSikp 065b7uVyOi7NIeXaioo+Ehkkg1zHdQYz41JDN+LkqO+3f87veTzzfJ/5Pb/f 5/N43q9ZccB3xyFZBoNxc/7v0+f/X7l2LuLAe6Og9PnUj8ywG3bmZ3IsybdS yCHf48Tcp6sP1bh79NXHM3Dc8xXniuJDsAp4UNO+PwsVM2cUlryvAKtcndHU VbfRIYZh+L1/FbiH1BzQ2ZqHe1MKnarmaoBryq6t3VOAb0RdII2pB5doj+qN 5oVoeGDobqhBIxTsufpy7FEhnmnRbyw82ARSp9LloaOFaL7u09UCYno+7Pnp GoZser+NpreWvr0IHOnzzmTJx7n9KIYK+r6FPylKLy2VgBWdxzApbnQRYwS0 6bwFfDQ9LZg/0302ffu43LxyFKQ1ZF+9xZuVGm+MwTmJw7vXeUV4Wq55rvxe MQZnnt0rE1aCypHWZkrfPkTrXddM6jhlWBC8tO7jdxUYHRGifnOuArv+Kt2y JaoSjY+cW5Nd+wTHzv69fbinCtck2tzelv8UtQ7uXxfKrMFsrR+PvcirxaeT k7Vt6rVYGfir7IWnz9A5uuyPrLd1WCEcveRlI8BXGqti0my6cM1ScyOxuhBF nKaE+7p81Grt9AgWCtGP8QjnXvGR6f1HZknpIE79nGc7w+nGQybhuaqxQ1gS IRdoZdODk3onWxb6DuOtgMjnvi09yDXebrXMQYTFTot/NtvWix8ztGzqTcSo lXU6cfvtXgx8l/HDB1kRBDXM3hkVt+POP5uezHUMgWNwQtWt5624bKxigX3Z IGgbqbDcr7eg5X23gMhcIeihgZObTRP6cHZ5ueUKwPjOxV3yDxqQ+Q/DCJey ARi7kVh/ppiLbUaHY5j8fmBydkaqXn6CwZ0a/dOK/cC60hdQ7FSGXKdpvzLe E0i+7KMw7dQHW4+Ov93XWAFxu18dOqE4AFMpBjHOumWQb7/mp3I/AUSn+MWx WSXAPLzegjkohKld6SfN+EXw7qhuctDeIXCXUTr9/vs8uDTDCmHxh6G/0XLC oCgL0kKnnF1+E4OUuaW69XgGlDbb2L4XSaCBY88d4w+BcrxZ+HllAbqUlWv0 7BuECIsd4bNXBKhgaRVp3yUAtdSGpPdSAULUSLbejgFIf+0bZWIjxKnMZqOU iD5YsIDjGhAmRM0+1X+6+naD8u6S1ekPhCif067vad8JRVcPBcW2C/FvzFx2 wqo2SMqrMrAYEOIP5Iwx9KxG7sdser82eR7K0ufJ3vz8PvwgR95nTebBODqP CpkXZem8rmQfPEf34ZF98UMc2Veb9A86tAdH0gsA7cWR9AS5tKfjpDcwoL3x SI+wgPboTnoFf9prKekZrGnPU6R38KC9Uw9gHfWAegEnqRfUE1hBPaHegJh6 40jncaQeGdN5ralXxnSfjxnEMwbdt516x3NpXST3vBL+8jzfdurNKHirLI0d O1UDyyu2CX4RjYBdyL6ou+J6YF+T/874mQQG9V4PdH3Ngz9/S1iZnymGYHuZ WZZ6M8ge7U+46COCrYudS63ftEBh1pCfm+EwFJgLcvvvtQJL8otQbmAQ3IbZ arK726FHOpNnFiaEjVNJ9baVw6DtZTTZWxEKPRPdXpkhIuAlvXXTvJaGJtNr NXkmYuCe8jMZSbiLG6cl33g1iiGNxW9y0kYsXDG4RMNVArP5CUfenajG5NT2 42dfSMD0pVBB4F2PRReszV3Wj8CvShO5BY94yJiVizh2dQQuc64mvmxswX7S AxbRHipIL5hKe7EiPWEw7UlMesPXtDfaIyp+6ZH0il96dSQ9YyztmfaOqbT3 EOIBStnEgy7iBYpvEi8WEU+wknpygniDCtSbTcQjVKUeaROvcCH1yoV4hmbU s/PEOzxIvTvnEPV7qrsEv7mgFOwY24XrO7hlFtViLOj2WbvBohMr9+tmPF4h xmSYTA6eaMcrt0qEMf4iZHN09vWUtuG/197vVqsaxtlNHvHKMa2ofZi9IZs5 jJ72Dp7lgS/worxSQ/W2IYxmy6fE+7fgh/FKff7lQeSWpK9fHdqMbU0dXO3e 5vl9dj4MGriH0wc2+unO77HyyP3sJb/fRbveaZUR20ZkfFwoI2NVgOwQWKzy vh55+ZEZurwc1DpmOnonhou8JKHRbDUHhYnxO58tq0bW5vjwix7pyPZdneb/ r8fzvzN1Pil7U9B7+38Vg+b/P9GRp67r2SZgHfVgsj1WIiviozP1QhrmKpGX duFX1JORGo9nasu70JJ6w9XSFqae6MRJ4h8ypoq3fj3agWrUK+n2mP+Uh3Ug 44tn/aZf8R07UIN615HhnxO+oQMNqIdietakXpbS+/Wopwr25HkKxD/Qou+z oR4P0nlUqdfyXDKvG/VcI5zs00K91+wg+87OfO4Bd9Me8kgvaEB7SSQ9oWCc 9JRLesM7tDcW6REVaI+rSK/Ior22kZ4x7TrpmUV6R3cf0rsj8QCHqQcZxAvc TL2wIJ5gKfXEj3iDTOrNC+IRRlOPVhKvMIJ6ZUc8Qx3qWQHxDh9Q7/4HvCaR vw== "], { {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[Medium], ArrowBox[ BezierCurveBox[{1, {-0.16444074718311624`, 0.49999999999999967`}, 3}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{1, {-0.3507923283006618, -0.3924098644778737}, 4}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{2, {0.18635158111754768`, 0.10759013552212278`}, 3}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{2, {-1.8505415028554895`*^-15, -0.7848197289557458}, 4}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{3, {0.16444074718311655`, 0.5000000000000007}, 1}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{3, {0.6796738226668931, 0.39240986447787535`}, 2}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{3, {-0.18635158111754535`, 0.10759013552212827`}, 4}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{4, {-0.5152330754837754, -0.10759013552212586`}, 1}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{4, {-4.742012601067197*^-15, -0.2151802710442545}, 2}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{4, {-0.6796738226668936, 0.3924098644778727}, 3}], 0.020399597244776413`]}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], DiskBox[1, 0.020399597244776413], DiskBox[2, 0.020399597244776413], DiskBox[3, 0.020399597244776413], DiskBox[4, 0.020399597244776413]}}]], MouseAppearanceTag["NetworkGraphics"]], AllowKernelInitialization->False]], DefaultBaseStyle->"NetworkGraphics", FormatType->TraditionalForm, FrameTicks->None, ImageSize->{89.39999999999998, Automatic}]\)]
Out[2]=

Test whether a graph is a in-regular graph:

In[3]:=
ResourceFunction["RegularGraphQ"][\!\(\* GraphicsBox[ NamespaceBox["NetworkGraphics", DynamicModuleBox[{Typeset`graph = HoldComplete[ Graph[{1, 2, 3, 4}, { SparseArray[ Automatic, {4, 4}, 0, {1, {{0, 3, 6, 9, 12}, {{2}, {3}, {4}, {1}, {3}, {4}, { 1}, {2}, {4}, {1}, {2}, {3}}}, Pattern}], Null}, {GraphLayout -> {"Dimension" -> 2, "VertexLayout" -> "StarEmbedding"}, ImageSize -> {89.39999999999998, Automatic}}]]}, TagBox[GraphicsGroupBox[GraphicsComplexBox[CompressedData[" 1:eJxdlnlUDdoex49yG06GkOQZbh7FylDR7Z0y/OLl5hpS3EumhMQ1VPJkJtHh NmlQNDwv5dwylMpQKL+kdCo0aVCizmk4DTgyVPR04/fz/nh7rbPO2uvstffv t/f6fs5n3Ea3ZZtVBAJBTt/n6/f/j8TFDooDt9pA69usDoW+5xdb7L88i35V wmX6Hd/2fh0vMXDJfzUPG2RAXcCec4aLwjDMbUqM57/vg3ZDgWvU2ijsDD+z /NGYXHCfd8bvmPMFnLLTrO1qsBQEkXLjnlwJRnjDsIGdhWCSHBBrUHwZ17/o Hti6qAgmfVHv188qGVU3zfEwsCkBp623E0b+fh3rS6qk+i9KQXR1+d3D9bdQ 8Dp7Ys2JBpClXZg5xacUT6lpPc5d2AhJYrWoM55laLhFPDtB2ATetktdMg88 Rcn028+1c5pg9DznMwOCyzHgUpo82LMZ/pSMX1ebXoHSDQax98cpIAM6Ir3e 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{0.18635158111754768`, 0.10759013552212278`}, 3}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{2, {-1.8505415028554895`*^-15, -0.7848197289557458}, 4}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{3, {0.16444074718311655`, 0.5000000000000007}, 1}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{3, {0.6796738226668931, 0.39240986447787535`}, 2}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{3, {-0.18635158111754535`, 0.10759013552212827`}, 4}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{4, {-0.5152330754837754, -0.10759013552212586`}, 1}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{4, {-4.742012601067197*^-15, -0.2151802710442545}, 2}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{4, {-0.6796738226668936, 0.3924098644778727}, 3}], 0.020399597244776413`]}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], DiskBox[1, 0.020399597244776413], DiskBox[2, 0.020399597244776413], DiskBox[3, 0.020399597244776413], DiskBox[4, 0.020399597244776413]}}]], MouseAppearanceTag["NetworkGraphics"]], AllowKernelInitialization->False]], DefaultBaseStyle->"NetworkGraphics", FormatType->TraditionalForm, FrameTicks->None, ImageSize->{89.39999999999998, Automatic}]\), "In"]
Out[3]=
In[4]:=
ResourceFunction["RegularGraphQ"][\!\(\* GraphicsBox[ NamespaceBox["NetworkGraphics", DynamicModuleBox[{Typeset`graph = HoldComplete[ Graph[{1, 2, 3, 4}, { SparseArray[ Automatic, {4, 4}, 0, {1, {{0, 2, 4, 7, 10}, {{3}, {4}, {3}, {4}, {1}, {2}, { 4}, {1}, {2}, {3}}}, Pattern}], Null}, {GraphLayout -> {"Dimension" -> 2}, VertexCoordinates -> {{0., 0.}, { 0.8660254037844389, -0.5000000000000012}, { 1.8369701987210297`*^-16, 1.}, {-0.8660254037844386, -0.49999999999999917`}}}]]}, TagBox[GraphicsGroupBox[GraphicsComplexBox[CompressedData[" 1:eJxd1Xs41PkewPFBKwaxslanrdVj0aOEss6Q+qij1UYutSulrEpqJUonSikp 065b7uVyOi7NIeXaioo+Ehkkg1zHdQYz41JDN+LkqO+3f87veTzzfJ/5Pb/f 5/N43q9ZccB3xyFZBoNxc/7v0+f/X7l2LuLAe6Og9PnUj8ywG3bmZ3IsybdS yCHf48Tcp6sP1bh79NXHM3Dc8xXniuJDsAp4UNO+PwsVM2cUlryvAKtcndHU VbfRIYZh+L1/FbiH1BzQ2ZqHe1MKnarmaoBryq6t3VOAb0RdII2pB5doj+qN 5oVoeGDobqhBIxTsufpy7FEhnmnRbyw82ARSp9LloaOFaL7u09UCYno+7Pnp GoZser+NpreWvr0IHOnzzmTJx7n9KIYK+r6FPylKLy2VgBWdxzApbnQRYwS0 6bwFfDQ9LZg/0302ffu43LxyFKQ1ZF+9xZuVGm+MwTmJw7vXeUV4Wq55rvxe MQZnnt0rE1aCypHWZkrfPkTrXddM6jhlWBC8tO7jdxUYHRGifnOuArv+Kt2y JaoSjY+cW5Nd+wTHzv69fbinCtck2tzelv8UtQ7uXxfKrMFsrR+PvcirxaeT k7Vt6rVYGfir7IWnz9A5uuyPrLd1WCEcveRlI8BXGqti0my6cM1ScyOxuhBF nKaE+7p81Grt9AgWCtGP8QjnXvGR6f1HZknpIE79nGc7w+nGQybhuaqxQ1gS IRdoZdODk3onWxb6DuOtgMjnvi09yDXebrXMQYTFTot/NtvWix8ztGzqTcSo lXU6cfvtXgx8l/HDB1kRBDXM3hkVt+POP5uezHUMgWNwQtWt5624bKxigX3Z IGgbqbDcr7eg5X23gMhcIeihgZObTRP6cHZ5ueUKwPjOxV3yDxqQ+Q/DCJey ARi7kVh/ppiLbUaHY5j8fmBydkaqXn6CwZ0a/dOK/cC60hdQ7FSGXKdpvzLe E0i+7KMw7dQHW4+Ov93XWAFxu18dOqE4AFMpBjHOumWQb7/mp3I/AUSn+MWx WSXAPLzegjkohKld6SfN+EXw7qhuctDeIXCXUTr9/vs8uDTDCmHxh6G/0XLC oCgL0kKnnF1+E4OUuaW69XgGlDbb2L4XSaCBY88d4w+BcrxZ+HllAbqUlWv0 7BuECIsd4bNXBKhgaRVp3yUAtdSGpPdSAULUSLbejgFIf+0bZWIjxKnMZqOU iD5YsIDjGhAmRM0+1X+6+naD8u6S1ekPhCif067vad8JRVcPBcW2C/FvzFx2 wqo2SMqrMrAYEOIP5Iwx9KxG7sdser82eR7K0ufJ3vz8PvwgR95nTebBODqP CpkXZem8rmQfPEf34ZF98UMc2Veb9A86tAdH0gsA7cWR9AS5tKfjpDcwoL3x SI+wgPboTnoFf9prKekZrGnPU6R38KC9Uw9gHfWAegEnqRfUE1hBPaHegJh6 40jncaQeGdN5ralXxnSfjxnEMwbdt516x3NpXST3vBL+8jzfdurNKHirLI0d O1UDyyu2CX4RjYBdyL6ou+J6YF+T/874mQQG9V4PdH3Ngz9/S1iZnymGYHuZ WZZ6M8ge7U+46COCrYudS63ftEBh1pCfm+EwFJgLcvvvtQJL8otQbmAQ3IbZ arK726FHOpNnFiaEjVNJ9baVw6DtZTTZWxEKPRPdXpkhIuAlvXXTvJaGJtNr NXkmYuCe8jMZSbiLG6cl33g1iiGNxW9y0kYsXDG4RMNVArP5CUfenajG5NT2 42dfSMD0pVBB4F2PRReszV3Wj8CvShO5BY94yJiVizh2dQQuc64mvmxswX7S AxbRHipIL5hKe7EiPWEw7UlMesPXtDfaIyp+6ZH0il96dSQ9YyztmfaOqbT3 EOIBStnEgy7iBYpvEi8WEU+wknpygniDCtSbTcQjVKUeaROvcCH1yoV4hmbU s/PEOzxIvTvnEPV7qrsEv7mgFOwY24XrO7hlFtViLOj2WbvBohMr9+tmPF4h xmSYTA6eaMcrt0qEMf4iZHN09vWUtuG/197vVqsaxtlNHvHKMa2ofZi9IZs5 jJ72Dp7lgS/worxSQ/W2IYxmy6fE+7fgh/FKff7lQeSWpK9fHdqMbU0dXO3e 5vl9dj4MGriH0wc2+unO77HyyP3sJb/fRbveaZUR20ZkfFwoI2NVgOwQWKzy vh55+ZEZurwc1DpmOnonhou8JKHRbDUHhYnxO58tq0bW5vjwix7pyPZdneb/ r8fzvzN1Pil7U9B7+38Vg+b/P9GRp67r2SZgHfVgsj1WIiviozP1QhrmKpGX duFX1JORGo9nasu70JJ6w9XSFqae6MRJ4h8ypoq3fj3agWrUK+n2mP+Uh3Ug 44tn/aZf8R07UIN615HhnxO+oQMNqIdietakXpbS+/Wopwr25HkKxD/Qou+z oR4P0nlUqdfyXDKvG/VcI5zs00K91+wg+87OfO4Bd9Me8kgvaEB7SSQ9oWCc 9JRLesM7tDcW6REVaI+rSK/Ior22kZ4x7TrpmUV6R3cf0rsj8QCHqQcZxAvc TL2wIJ5gKfXEj3iDTOrNC+IRRlOPVhKvMIJ6ZUc8Qx3qWQHxDh9Q7/4HvCaR vw== "], { {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[Medium], ArrowBox[ BezierCurveBox[{1, {-0.16444074718311624`, 0.49999999999999967`}, 3}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{1, {-0.3507923283006618, -0.3924098644778737}, 4}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{2, {0.18635158111754768`, 0.10759013552212278`}, 3}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{2, {-1.8505415028554895`*^-15, -0.7848197289557458}, 4}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{3, {0.16444074718311655`, 0.5000000000000007}, 1}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{3, {0.6796738226668931, 0.39240986447787535`}, 2}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{3, {-0.18635158111754535`, 0.10759013552212827`}, 4}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{4, {-0.5152330754837754, -0.10759013552212586`}, 1}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{4, {-4.742012601067197*^-15, -0.2151802710442545}, 2}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{4, {-0.6796738226668936, 0.3924098644778727}, 3}], 0.020399597244776413`]}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], DiskBox[1, 0.020399597244776413], DiskBox[2, 0.020399597244776413], DiskBox[3, 0.020399597244776413], DiskBox[4, 0.020399597244776413]}}]], MouseAppearanceTag["NetworkGraphics"]], AllowKernelInitialization->False]], DefaultBaseStyle->"NetworkGraphics", FormatType->TraditionalForm, FrameTicks->None, ImageSize->{89.39999999999998, Automatic}]\), "In"]
Out[4]=

Test whether a graph is a out-regular graph:

In[5]:=
ResourceFunction["RegularGraphQ"][\!\(\* GraphicsBox[ NamespaceBox["NetworkGraphics", DynamicModuleBox[{Typeset`graph = HoldComplete[ Graph[{1, 2, 3, 4}, { SparseArray[ Automatic, {4, 4}, 0, {1, {{0, 3, 6, 9, 12}, {{2}, {3}, {4}, {1}, {3}, {4}, { 1}, {2}, {4}, {1}, {2}, {3}}}, Pattern}], Null}, {GraphLayout -> {"Dimension" -> 2, "VertexLayout" -> "StarEmbedding"}, ImageSize -> {89.39999999999998, Automatic}}]]}, TagBox[GraphicsGroupBox[GraphicsComplexBox[CompressedData[" 1:eJxdlnlUDdoex49yG06GkOQZbh7FylDR7Z0y/OLl5hpS3EumhMQ1VPJkJtHh NmlQNDwv5dwylMpQKL+kdCo0aVCizmk4DTgyVPR04/fz/nh7rbPO2uvstffv t/f6fs5n3Ea3ZZtVBAJBTt/n6/f/j8TFDooDt9pA69usDoW+5xdb7L88i35V wmX6Hd/2fh0vMXDJfzUPG2RAXcCec4aLwjDMbUqM57/vg3ZDgWvU2ijsDD+z /NGYXHCfd8bvmPMFnLLTrO1qsBQEkXLjnlwJRnjDsIGdhWCSHBBrUHwZ17/o Hti6qAgmfVHv188qGVU3zfEwsCkBp623E0b+fh3rS6qk+i9KQXR1+d3D9bdQ 8Dp7Ys2JBpClXZg5xacUT6lpPc5d2AhJYrWoM55laLhFPDtB2ATetktdMg88 Rcn028+1c5pg9DznMwOCyzHgUpo82LMZ/pSMX1ebXoHSDQax98cpIAM6Ir3e 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{0.18635158111754768`, 0.10759013552212278`}, 3}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{2, {-1.8505415028554895`*^-15, -0.7848197289557458}, 4}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{3, {0.16444074718311655`, 0.5000000000000007}, 1}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{3, {0.6796738226668931, 0.39240986447787535`}, 2}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{3, {-0.18635158111754535`, 0.10759013552212827`}, 4}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{4, {-0.5152330754837754, -0.10759013552212586`}, 1}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{4, {-4.742012601067197*^-15, -0.2151802710442545}, 2}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{4, {-0.6796738226668936, 0.3924098644778727}, 3}], 0.020399597244776413`]}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], DiskBox[1, 0.020399597244776413], DiskBox[2, 0.020399597244776413], DiskBox[3, 0.020399597244776413], DiskBox[4, 0.020399597244776413]}}]], MouseAppearanceTag["NetworkGraphics"]], AllowKernelInitialization->False]], DefaultBaseStyle->"NetworkGraphics", FormatType->TraditionalForm, FrameTicks->None, ImageSize->{89.39999999999998, Automatic}]\), "Out"]
Out[5]=
In[6]:=
ResourceFunction["RegularGraphQ"][\!\(\* GraphicsBox[ NamespaceBox["NetworkGraphics", DynamicModuleBox[{Typeset`graph = HoldComplete[ Graph[{1, 2, 3, 4}, { SparseArray[ Automatic, {4, 4}, 0, {1, {{0, 2, 4, 7, 10}, {{3}, {4}, {3}, {4}, {1}, {2}, { 4}, {1}, {2}, {3}}}, Pattern}], Null}, {GraphLayout -> {"Dimension" -> 2}, VertexCoordinates -> {{0., 0.}, { 0.8660254037844389, -0.5000000000000012}, { 1.8369701987210297`*^-16, 1.}, {-0.8660254037844386, -0.49999999999999917`}}}]]}, TagBox[GraphicsGroupBox[GraphicsComplexBox[CompressedData[" 1:eJxd1Xs41PkewPFBKwaxslanrdVj0aOEss6Q+qij1UYutSulrEpqJUonSikp 065b7uVyOi7NIeXaioo+Ehkkg1zHdQYz41JDN+LkqO+3f87veTzzfJ/5Pb/f 5/N43q9ZccB3xyFZBoNxc/7v0+f/X7l2LuLAe6Og9PnUj8ywG3bmZ3IsybdS yCHf48Tcp6sP1bh79NXHM3Dc8xXniuJDsAp4UNO+PwsVM2cUlryvAKtcndHU VbfRIYZh+L1/FbiH1BzQ2ZqHe1MKnarmaoBryq6t3VOAb0RdII2pB5doj+qN 5oVoeGDobqhBIxTsufpy7FEhnmnRbyw82ARSp9LloaOFaL7u09UCYno+7Pnp GoZser+NpreWvr0IHOnzzmTJx7n9KIYK+r6FPylKLy2VgBWdxzApbnQRYwS0 6bwFfDQ9LZg/0302ffu43LxyFKQ1ZF+9xZuVGm+MwTmJw7vXeUV4Wq55rvxe MQZnnt0rE1aCypHWZkrfPkTrXddM6jhlWBC8tO7jdxUYHRGifnOuArv+Kt2y JaoSjY+cW5Nd+wTHzv69fbinCtck2tzelv8UtQ7uXxfKrMFsrR+PvcirxaeT k7Vt6rVYGfir7IWnz9A5uuyPrLd1WCEcveRlI8BXGqti0my6cM1ScyOxuhBF nKaE+7p81Grt9AgWCtGP8QjnXvGR6f1HZknpIE79nGc7w+nGQybhuaqxQ1gS IRdoZdODk3onWxb6DuOtgMjnvi09yDXebrXMQYTFTot/NtvWix8ztGzqTcSo lXU6cfvtXgx8l/HDB1kRBDXM3hkVt+POP5uezHUMgWNwQtWt5624bKxigX3Z IGgbqbDcr7eg5X23gMhcIeihgZObTRP6cHZ5ueUKwPjOxV3yDxqQ+Q/DCJey ARi7kVh/ppiLbUaHY5j8fmBydkaqXn6CwZ0a/dOK/cC60hdQ7FSGXKdpvzLe E0i+7KMw7dQHW4+Ov93XWAFxu18dOqE4AFMpBjHOumWQb7/mp3I/AUSn+MWx WSXAPLzegjkohKld6SfN+EXw7qhuctDeIXCXUTr9/vs8uDTDCmHxh6G/0XLC oCgL0kKnnF1+E4OUuaW69XgGlDbb2L4XSaCBY88d4w+BcrxZ+HllAbqUlWv0 7BuECIsd4bNXBKhgaRVp3yUAtdSGpPdSAULUSLbejgFIf+0bZWIjxKnMZqOU iD5YsIDjGhAmRM0+1X+6+naD8u6S1ekPhCif067vad8JRVcPBcW2C/FvzFx2 wqo2SMqrMrAYEOIP5Iwx9KxG7sdser82eR7K0ufJ3vz8PvwgR95nTebBODqP CpkXZem8rmQfPEf34ZF98UMc2Veb9A86tAdH0gsA7cWR9AS5tKfjpDcwoL3x SI+wgPboTnoFf9prKekZrGnPU6R38KC9Uw9gHfWAegEnqRfUE1hBPaHegJh6 40jncaQeGdN5ralXxnSfjxnEMwbdt516x3NpXST3vBL+8jzfdurNKHirLI0d O1UDyyu2CX4RjYBdyL6ou+J6YF+T/874mQQG9V4PdH3Ngz9/S1iZnymGYHuZ WZZ6M8ge7U+46COCrYudS63ftEBh1pCfm+EwFJgLcvvvtQJL8otQbmAQ3IbZ arK726FHOpNnFiaEjVNJ9baVw6DtZTTZWxEKPRPdXpkhIuAlvXXTvJaGJtNr NXkmYuCe8jMZSbiLG6cl33g1iiGNxW9y0kYsXDG4RMNVArP5CUfenajG5NT2 42dfSMD0pVBB4F2PRReszV3Wj8CvShO5BY94yJiVizh2dQQuc64mvmxswX7S AxbRHipIL5hKe7EiPWEw7UlMesPXtDfaIyp+6ZH0il96dSQ9YyztmfaOqbT3 EOIBStnEgy7iBYpvEi8WEU+wknpygniDCtSbTcQjVKUeaROvcCH1yoV4hmbU s/PEOzxIvTvnEPV7qrsEv7mgFOwY24XrO7hlFtViLOj2WbvBohMr9+tmPF4h xmSYTA6eaMcrt0qEMf4iZHN09vWUtuG/197vVqsaxtlNHvHKMa2ofZi9IZs5 jJ72Dp7lgS/worxSQ/W2IYxmy6fE+7fgh/FKff7lQeSWpK9fHdqMbU0dXO3e 5vl9dj4MGriH0wc2+unO77HyyP3sJb/fRbveaZUR20ZkfFwoI2NVgOwQWKzy vh55+ZEZurwc1DpmOnonhou8JKHRbDUHhYnxO58tq0bW5vjwix7pyPZdneb/ r8fzvzN1Pil7U9B7+38Vg+b/P9GRp67r2SZgHfVgsj1WIiviozP1QhrmKpGX duFX1JORGo9nasu70JJ6w9XSFqae6MRJ4h8ypoq3fj3agWrUK+n2mP+Uh3Ug 44tn/aZf8R07UIN615HhnxO+oQMNqIdietakXpbS+/Wopwr25HkKxD/Qou+z oR4P0nlUqdfyXDKvG/VcI5zs00K91+wg+87OfO4Bd9Me8kgvaEB7SSQ9oWCc 9JRLesM7tDcW6REVaI+rSK/Ior22kZ4x7TrpmUV6R3cf0rsj8QCHqQcZxAvc TL2wIJ5gKfXEj3iDTOrNC+IRRlOPVhKvMIJ6ZUc8Qx3qWQHxDh9Q7/4HvCaR vw== "], { {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[Medium], ArrowBox[ BezierCurveBox[{1, {-0.16444074718311624`, 0.49999999999999967`}, 3}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{1, {-0.3507923283006618, -0.3924098644778737}, 4}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{2, {0.18635158111754768`, 0.10759013552212278`}, 3}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{2, {-1.8505415028554895`*^-15, -0.7848197289557458}, 4}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{3, {0.16444074718311655`, 0.5000000000000007}, 1}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{3, {0.6796738226668931, 0.39240986447787535`}, 2}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{3, {-0.18635158111754535`, 0.10759013552212827`}, 4}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{4, {-0.5152330754837754, -0.10759013552212586`}, 1}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{4, {-4.742012601067197*^-15, -0.2151802710442545}, 2}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{4, {-0.6796738226668936, 0.3924098644778727}, 3}], 0.020399597244776413`]}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], DiskBox[1, 0.020399597244776413], DiskBox[2, 0.020399597244776413], DiskBox[3, 0.020399597244776413], DiskBox[4, 0.020399597244776413]}}]], MouseAppearanceTag["NetworkGraphics"]], AllowKernelInitialization->False]], DefaultBaseStyle->"NetworkGraphics", FormatType->TraditionalForm, FrameTicks->None, ImageSize->{89.39999999999998, Automatic}]\), "Out"]
Out[6]=

Test whether a graph is a k-regular graph:

In[7]:=
ResourceFunction["RegularGraphQ"][\!\(\* GraphicsBox[ NamespaceBox["NetworkGraphics", DynamicModuleBox[{Typeset`graph = HoldComplete[ Graph[{1, 2, 3, 4}, {Null, SparseArray[ Automatic, {4, 4}, 0, {1, {{0, 3, 6, 9, 12}, {{2}, {3}, {4}, {1}, {3}, {4}, { 1}, {2}, {4}, {1}, {2}, {3}}}, Pattern}]}, {GraphLayout -> "StarEmbedding"}]]}, TagBox[GraphicsGroupBox[ GraphicsComplexBox[{{0., 0.}, { 0.8660254037844389, -0.5000000000000012}, { 1.8369701987210297`*^-16, 1.}, {-0.8660254037844386, -0.49999999999999917`}}, { {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[0.], ArrowBox[{{1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}}, 0.020399597244776413`]}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], DiskBox[1, 0.020399597244776413], DiskBox[2, 0.020399597244776413], DiskBox[3, 0.020399597244776413], DiskBox[4, 0.020399597244776413]}}]], MouseAppearanceTag["NetworkGraphics"]], AllowKernelInitialization->False]], DefaultBaseStyle->"NetworkGraphics", FormatType->TraditionalForm, FrameTicks->None, ImageSize->{89.39999999999998, Automatic}]\), 3]
Out[7]=
In[8]:=
ResourceFunction["RegularGraphQ"][\!\(\* GraphicsBox[ NamespaceBox["NetworkGraphics", DynamicModuleBox[{Typeset`graph = HoldComplete[ Graph[{1, 2, 3, 4}, { SparseArray[ Automatic, {4, 4}, 0, {1, {{0, 2, 4, 7, 10}, {{3}, {4}, {3}, {4}, {1}, {2}, { 4}, {1}, {2}, {3}}}, Pattern}], Null}, {GraphLayout -> {"Dimension" -> 2}, VertexCoordinates -> {{0., 0.}, { 0.8660254037844389, -0.5000000000000012}, { 1.8369701987210297`*^-16, 1.}, {-0.8660254037844386, -0.49999999999999917`}}}]]}, TagBox[GraphicsGroupBox[GraphicsComplexBox[CompressedData[" 1:eJxd1Xs41PkewPFBKwaxslanrdVj0aOEss6Q+qij1UYutSulrEpqJUonSikp 065b7uVyOi7NIeXaioo+Ehkkg1zHdQYz41JDN+LkqO+3f87veTzzfJ/5Pb/f 5/N43q9ZccB3xyFZBoNxc/7v0+f/X7l2LuLAe6Og9PnUj8ywG3bmZ3IsybdS yCHf48Tcp6sP1bh79NXHM3Dc8xXniuJDsAp4UNO+PwsVM2cUlryvAKtcndHU VbfRIYZh+L1/FbiH1BzQ2ZqHe1MKnarmaoBryq6t3VOAb0RdII2pB5doj+qN 5oVoeGDobqhBIxTsufpy7FEhnmnRbyw82ARSp9LloaOFaL7u09UCYno+7Pnp GoZser+NpreWvr0IHOnzzmTJx7n9KIYK+r6FPylKLy2VgBWdxzApbnQRYwS0 6bwFfDQ9LZg/0302ffu43LxyFKQ1ZF+9xZuVGm+MwTmJw7vXeUV4Wq55rvxe MQZnnt0rE1aCypHWZkrfPkTrXddM6jhlWBC8tO7jdxUYHRGifnOuArv+Kt2y JaoSjY+cW5Nd+wTHzv69fbinCtck2tzelv8UtQ7uXxfKrMFsrR+PvcirxaeT k7Vt6rVYGfir7IWnz9A5uuyPrLd1WCEcveRlI8BXGqti0my6cM1ScyOxuhBF nKaE+7p81Grt9AgWCtGP8QjnXvGR6f1HZknpIE79nGc7w+nGQybhuaqxQ1gS IRdoZdODk3onWxb6DuOtgMjnvi09yDXebrXMQYTFTot/NtvWix8ztGzqTcSo lXU6cfvtXgx8l/HDB1kRBDXM3hkVt+POP5uezHUMgWNwQtWt5624bKxigX3Z IGgbqbDcr7eg5X23gMhcIeihgZObTRP6cHZ5ueUKwPjOxV3yDxqQ+Q/DCJey ARi7kVh/ppiLbUaHY5j8fmBydkaqXn6CwZ0a/dOK/cC60hdQ7FSGXKdpvzLe E0i+7KMw7dQHW4+Ov93XWAFxu18dOqE4AFMpBjHOumWQb7/mp3I/AUSn+MWx WSXAPLzegjkohKld6SfN+EXw7qhuctDeIXCXUTr9/vs8uDTDCmHxh6G/0XLC oCgL0kKnnF1+E4OUuaW69XgGlDbb2L4XSaCBY88d4w+BcrxZ+HllAbqUlWv0 7BuECIsd4bNXBKhgaRVp3yUAtdSGpPdSAULUSLbejgFIf+0bZWIjxKnMZqOU iD5YsIDjGhAmRM0+1X+6+naD8u6S1ekPhCif067vad8JRVcPBcW2C/FvzFx2 wqo2SMqrMrAYEOIP5Iwx9KxG7sdser82eR7K0ufJ3vz8PvwgR95nTebBODqP CpkXZem8rmQfPEf34ZF98UMc2Veb9A86tAdH0gsA7cWR9AS5tKfjpDcwoL3x SI+wgPboTnoFf9prKekZrGnPU6R38KC9Uw9gHfWAegEnqRfUE1hBPaHegJh6 40jncaQeGdN5ralXxnSfjxnEMwbdt516x3NpXST3vBL+8jzfdurNKHirLI0d O1UDyyu2CX4RjYBdyL6ou+J6YF+T/874mQQG9V4PdH3Ngz9/S1iZnymGYHuZ WZZ6M8ge7U+46COCrYudS63ftEBh1pCfm+EwFJgLcvvvtQJL8otQbmAQ3IbZ arK726FHOpNnFiaEjVNJ9baVw6DtZTTZWxEKPRPdXpkhIuAlvXXTvJaGJtNr NXkmYuCe8jMZSbiLG6cl33g1iiGNxW9y0kYsXDG4RMNVArP5CUfenajG5NT2 42dfSMD0pVBB4F2PRReszV3Wj8CvShO5BY94yJiVizh2dQQuc64mvmxswX7S AxbRHipIL5hKe7EiPWEw7UlMesPXtDfaIyp+6ZH0il96dSQ9YyztmfaOqbT3 EOIBStnEgy7iBYpvEi8WEU+wknpygniDCtSbTcQjVKUeaROvcCH1yoV4hmbU s/PEOzxIvTvnEPV7qrsEv7mgFOwY24XrO7hlFtViLOj2WbvBohMr9+tmPF4h xmSYTA6eaMcrt0qEMf4iZHN09vWUtuG/197vVqsaxtlNHvHKMa2ofZi9IZs5 jJ72Dp7lgS/worxSQ/W2IYxmy6fE+7fgh/FKff7lQeSWpK9fHdqMbU0dXO3e 5vl9dj4MGriH0wc2+unO77HyyP3sJb/fRbveaZUR20ZkfFwoI2NVgOwQWKzy vh55+ZEZurwc1DpmOnonhou8JKHRbDUHhYnxO58tq0bW5vjwix7pyPZdneb/ r8fzvzN1Pil7U9B7+38Vg+b/P9GRp67r2SZgHfVgsj1WIiviozP1QhrmKpGX duFX1JORGo9nasu70JJ6w9XSFqae6MRJ4h8ypoq3fj3agWrUK+n2mP+Uh3Ug 44tn/aZf8R07UIN615HhnxO+oQMNqIdietakXpbS+/Wopwr25HkKxD/Qou+z oR4P0nlUqdfyXDKvG/VcI5zs00K91+wg+87OfO4Bd9Me8kgvaEB7SSQ9oWCc 9JRLesM7tDcW6REVaI+rSK/Ior22kZ4x7TrpmUV6R3cf0rsj8QCHqQcZxAvc TL2wIJ5gKfXEj3iDTOrNC+IRRlOPVhKvMIJ6ZUc8Qx3qWQHxDh9Q7/4HvCaR vw== "], { {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[Medium], ArrowBox[ BezierCurveBox[{1, {-0.16444074718311624`, 0.49999999999999967`}, 3}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{1, {-0.3507923283006618, -0.3924098644778737}, 4}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{2, {0.18635158111754768`, 0.10759013552212278`}, 3}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{2, {-1.8505415028554895`*^-15, -0.7848197289557458}, 4}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{3, {0.16444074718311655`, 0.5000000000000007}, 1}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{3, {0.6796738226668931, 0.39240986447787535`}, 2}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{3, {-0.18635158111754535`, 0.10759013552212827`}, 4}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{4, {-0.5152330754837754, -0.10759013552212586`}, 1}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{4, {-4.742012601067197*^-15, -0.2151802710442545}, 2}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{4, {-0.6796738226668936, 0.3924098644778727}, 3}], 0.020399597244776413`]}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], DiskBox[1, 0.020399597244776413], DiskBox[2, 0.020399597244776413], DiskBox[3, 0.020399597244776413], DiskBox[4, 0.020399597244776413]}}]], MouseAppearanceTag["NetworkGraphics"]], AllowKernelInitialization->False]], DefaultBaseStyle->"NetworkGraphics", FormatType->TraditionalForm, FrameTicks->None, ImageSize->{89.39999999999998, Automatic}]\), 3]
Out[8]=

Test whether a graph is a k-In-regular graph:

In[9]:=
ResourceFunction["RegularGraphQ"][\!\(\* GraphicsBox[ NamespaceBox["NetworkGraphics", DynamicModuleBox[{Typeset`graph = HoldComplete[ Graph[{1, 2, 3, 4}, { SparseArray[ Automatic, {4, 4}, 0, {1, {{0, 3, 6, 9, 12}, {{2}, {3}, {4}, {1}, {3}, {4}, { 1}, {2}, {4}, {1}, {2}, {3}}}, Pattern}], Null}, {GraphLayout -> {"Dimension" -> 2, "VertexLayout" -> "StarEmbedding"}, ImageSize -> {89.39999999999998, Automatic}}]]}, TagBox[GraphicsGroupBox[GraphicsComplexBox[CompressedData[" 1:eJxdlnlUDdoex49yG06GkOQZbh7FylDR7Z0y/OLl5hpS3EumhMQ1VPJkJtHh NmlQNDwv5dwylMpQKL+kdCo0aVCizmk4DTgyVPR04/fz/nh7rbPO2uvstffv t/f6fs5n3Ea3ZZtVBAJBTt/n6/f/j8TFDooDt9pA69usDoW+5xdb7L88i35V wmX6Hd/2fh0vMXDJfzUPG2RAXcCec4aLwjDMbUqM57/vg3ZDgWvU2ijsDD+z /NGYXHCfd8bvmPMFnLLTrO1qsBQEkXLjnlwJRnjDsIGdhWCSHBBrUHwZ17/o Hti6qAgmfVHv188qGVU3zfEwsCkBp623E0b+fh3rS6qk+i9KQXR1+d3D9bdQ 8Dp7Ys2JBpClXZg5xacUT6lpPc5d2AhJYrWoM55laLhFPDtB2ATetktdMg88 Rcn028+1c5pg9DznMwOCyzHgUpo82LMZ/pSMX1ebXoHSDQax98cpIAM6Ir3e 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0.020399597244776413]}}]], MouseAppearanceTag["NetworkGraphics"]], AllowKernelInitialization->False]], DefaultBaseStyle->"NetworkGraphics", FormatType->TraditionalForm, FrameTicks->None, ImageSize->{89.39999999999998, Automatic}]\), 3, "In"]
Out[9]=
In[10]:=
ResourceFunction["RegularGraphQ"][\!\(\* GraphicsBox[ NamespaceBox["NetworkGraphics", DynamicModuleBox[{Typeset`graph = HoldComplete[ Graph[{1, 2, 3, 4}, { SparseArray[ Automatic, {4, 4}, 0, {1, {{0, 2, 4, 7, 10}, {{3}, {4}, {3}, {4}, {1}, {2}, { 4}, {1}, {2}, {3}}}, Pattern}], Null}, {GraphLayout -> {"Dimension" -> 2}, VertexCoordinates -> {{0., 0.}, { 0.8660254037844389, -0.5000000000000012}, { 1.8369701987210297`*^-16, 1.}, {-0.8660254037844386, -0.49999999999999917`}}}]]}, TagBox[GraphicsGroupBox[GraphicsComplexBox[CompressedData[" 1:eJxd1Xs41PkewPFBKwaxslanrdVj0aOEss6Q+qij1UYutSulrEpqJUonSikp 065b7uVyOi7NIeXaioo+Ehkkg1zHdQYz41JDN+LkqO+3f87veTzzfJ/5Pb/f 5/N43q9ZccB3xyFZBoNxc/7v0+f/X7l2LuLAe6Og9PnUj8ywG3bmZ3IsybdS yCHf48Tcp6sP1bh79NXHM3Dc8xXniuJDsAp4UNO+PwsVM2cUlryvAKtcndHU VbfRIYZh+L1/FbiH1BzQ2ZqHe1MKnarmaoBryq6t3VOAb0RdII2pB5doj+qN 5oVoeGDobqhBIxTsufpy7FEhnmnRbyw82ARSp9LloaOFaL7u09UCYno+7Pnp GoZser+NpreWvr0IHOnzzmTJx7n9KIYK+r6FPylKLy2VgBWdxzApbnQRYwS0 6bwFfDQ9LZg/0302ffu43LxyFKQ1ZF+9xZuVGm+MwTmJw7vXeUV4Wq55rvxe MQZnnt0rE1aCypHWZkrfPkTrXddM6jhlWBC8tO7jdxUYHRGifnOuArv+Kt2y JaoSjY+cW5Nd+wTHzv69fbinCtck2tzelv8UtQ7uXxfKrMFsrR+PvcirxaeT k7Vt6rVYGfir7IWnz9A5uuyPrLd1WCEcveRlI8BXGqti0my6cM1ScyOxuhBF nKaE+7p81Grt9AgWCtGP8QjnXvGR6f1HZknpIE79nGc7w+nGQybhuaqxQ1gS IRdoZdODk3onWxb6DuOtgMjnvi09yDXebrXMQYTFTot/NtvWix8ztGzqTcSo lXU6cfvtXgx8l/HDB1kRBDXM3hkVt+POP5uezHUMgWNwQtWt5624bKxigX3Z IGgbqbDcr7eg5X23gMhcIeihgZObTRP6cHZ5ueUKwPjOxV3yDxqQ+Q/DCJey ARi7kVh/ppiLbUaHY5j8fmBydkaqXn6CwZ0a/dOK/cC60hdQ7FSGXKdpvzLe E0i+7KMw7dQHW4+Ov93XWAFxu18dOqE4AFMpBjHOumWQb7/mp3I/AUSn+MWx WSXAPLzegjkohKld6SfN+EXw7qhuctDeIXCXUTr9/vs8uDTDCmHxh6G/0XLC oCgL0kKnnF1+E4OUuaW69XgGlDbb2L4XSaCBY88d4w+BcrxZ+HllAbqUlWv0 7BuECIsd4bNXBKhgaRVp3yUAtdSGpPdSAULUSLbejgFIf+0bZWIjxKnMZqOU iD5YsIDjGhAmRM0+1X+6+naD8u6S1ekPhCif067vad8JRVcPBcW2C/FvzFx2 wqo2SMqrMrAYEOIP5Iwx9KxG7sdser82eR7K0ufJ3vz8PvwgR95nTebBODqP CpkXZem8rmQfPEf34ZF98UMc2Veb9A86tAdH0gsA7cWR9AS5tKfjpDcwoL3x SI+wgPboTnoFf9prKekZrGnPU6R38KC9Uw9gHfWAegEnqRfUE1hBPaHegJh6 40jncaQeGdN5ralXxnSfjxnEMwbdt516x3NpXST3vBL+8jzfdurNKHirLI0d O1UDyyu2CX4RjYBdyL6ou+J6YF+T/874mQQG9V4PdH3Ngz9/S1iZnymGYHuZ WZZ6M8ge7U+46COCrYudS63ftEBh1pCfm+EwFJgLcvvvtQJL8otQbmAQ3IbZ arK726FHOpNnFiaEjVNJ9baVw6DtZTTZWxEKPRPdXpkhIuAlvXXTvJaGJtNr NXkmYuCe8jMZSbiLG6cl33g1iiGNxW9y0kYsXDG4RMNVArP5CUfenajG5NT2 42dfSMD0pVBB4F2PRReszV3Wj8CvShO5BY94yJiVizh2dQQuc64mvmxswX7S AxbRHipIL5hKe7EiPWEw7UlMesPXtDfaIyp+6ZH0il96dSQ9YyztmfaOqbT3 EOIBStnEgy7iBYpvEi8WEU+wknpygniDCtSbTcQjVKUeaROvcCH1yoV4hmbU s/PEOzxIvTvnEPV7qrsEv7mgFOwY24XrO7hlFtViLOj2WbvBohMr9+tmPF4h xmSYTA6eaMcrt0qEMf4iZHN09vWUtuG/197vVqsaxtlNHvHKMa2ofZi9IZs5 jJ72Dp7lgS/worxSQ/W2IYxmy6fE+7fgh/FKff7lQeSWpK9fHdqMbU0dXO3e 5vl9dj4MGriH0wc2+unO77HyyP3sJb/fRbveaZUR20ZkfFwoI2NVgOwQWKzy vh55+ZEZurwc1DpmOnonhou8JKHRbDUHhYnxO58tq0bW5vjwix7pyPZdneb/ r8fzvzN1Pil7U9B7+38Vg+b/P9GRp67r2SZgHfVgsj1WIiviozP1QhrmKpGX duFX1JORGo9nasu70JJ6w9XSFqae6MRJ4h8ypoq3fj3agWrUK+n2mP+Uh3Ug 44tn/aZf8R07UIN615HhnxO+oQMNqIdietakXpbS+/Wopwr25HkKxD/Qou+z oR4P0nlUqdfyXDKvG/VcI5zs00K91+wg+87OfO4Bd9Me8kgvaEB7SSQ9oWCc 9JRLesM7tDcW6REVaI+rSK/Ior22kZ4x7TrpmUV6R3cf0rsj8QCHqQcZxAvc TL2wIJ5gKfXEj3iDTOrNC+IRRlOPVhKvMIJ6ZUc8Qx3qWQHxDh9Q7/4HvCaR vw== "], { {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[Medium], ArrowBox[ BezierCurveBox[{1, {-0.16444074718311624`, 0.49999999999999967`}, 3}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{1, {-0.3507923283006618, -0.3924098644778737}, 4}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{2, {0.18635158111754768`, 0.10759013552212278`}, 3}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{2, {-1.8505415028554895`*^-15, -0.7848197289557458}, 4}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{3, {0.16444074718311655`, 0.5000000000000007}, 1}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{3, {0.6796738226668931, 0.39240986447787535`}, 2}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{3, {-0.18635158111754535`, 0.10759013552212827`}, 4}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{4, {-0.5152330754837754, -0.10759013552212586`}, 1}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{4, {-4.742012601067197*^-15, -0.2151802710442545}, 2}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{4, {-0.6796738226668936, 0.3924098644778727}, 3}], 0.020399597244776413`]}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], DiskBox[1, 0.020399597244776413], DiskBox[2, 0.020399597244776413], DiskBox[3, 0.020399597244776413], DiskBox[4, 0.020399597244776413]}}]], MouseAppearanceTag["NetworkGraphics"]], AllowKernelInitialization->False]], DefaultBaseStyle->"NetworkGraphics", FormatType->TraditionalForm, FrameTicks->None, ImageSize->{89.39999999999998, Automatic}]\), 2, "In"]
Out[10]=

Test whether a graph is a k-Out-regular graph:

In[11]:=
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{0.18635158111754768`, 0.10759013552212278`}, 3}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{2, {-1.8505415028554895`*^-15, -0.7848197289557458}, 4}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{3, {0.16444074718311655`, 0.5000000000000007}, 1}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{3, {0.6796738226668931, 0.39240986447787535`}, 2}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{3, {-0.18635158111754535`, 0.10759013552212827`}, 4}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{4, {-0.5152330754837754, -0.10759013552212586`}, 1}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{4, {-4.742012601067197*^-15, -0.2151802710442545}, 2}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{4, {-0.6796738226668936, 0.3924098644778727}, 3}], 0.020399597244776413`]}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], DiskBox[1, 0.020399597244776413], DiskBox[2, 0.020399597244776413], DiskBox[3, 0.020399597244776413], DiskBox[4, 0.020399597244776413]}}]], MouseAppearanceTag["NetworkGraphics"]], AllowKernelInitialization->False]], DefaultBaseStyle->"NetworkGraphics", FormatType->TraditionalForm, FrameTicks->None, ImageSize->{89.39999999999998, Automatic}]\), 3, "Out"]
Out[11]=
In[12]:=
ResourceFunction["RegularGraphQ"][\!\(\* GraphicsBox[ NamespaceBox["NetworkGraphics", DynamicModuleBox[{Typeset`graph = HoldComplete[ Graph[{1, 2, 3, 4}, { SparseArray[ Automatic, {4, 4}, 0, {1, {{0, 2, 4, 7, 10}, {{3}, {4}, {3}, {4}, {1}, {2}, { 4}, {1}, {2}, {3}}}, Pattern}], Null}, {GraphLayout -> {"Dimension" -> 2}, VertexCoordinates -> {{0., 0.}, { 0.8660254037844389, -0.5000000000000012}, { 1.8369701987210297`*^-16, 1.}, {-0.8660254037844386, -0.49999999999999917`}}}]]}, TagBox[GraphicsGroupBox[GraphicsComplexBox[CompressedData[" 1:eJxd1Xs41PkewPFBKwaxslanrdVj0aOEss6Q+qij1UYutSulrEpqJUonSikp 065b7uVyOi7NIeXaioo+Ehkkg1zHdQYz41JDN+LkqO+3f87veTzzfJ/5Pb/f 5/N43q9ZccB3xyFZBoNxc/7v0+f/X7l2LuLAe6Og9PnUj8ywG3bmZ3IsybdS yCHf48Tcp6sP1bh79NXHM3Dc8xXniuJDsAp4UNO+PwsVM2cUlryvAKtcndHU VbfRIYZh+L1/FbiH1BzQ2ZqHe1MKnarmaoBryq6t3VOAb0RdII2pB5doj+qN 5oVoeGDobqhBIxTsufpy7FEhnmnRbyw82ARSp9LloaOFaL7u09UCYno+7Pnp GoZser+NpreWvr0IHOnzzmTJx7n9KIYK+r6FPylKLy2VgBWdxzApbnQRYwS0 6bwFfDQ9LZg/0302ffu43LxyFKQ1ZF+9xZuVGm+MwTmJw7vXeUV4Wq55rvxe MQZnnt0rE1aCypHWZkrfPkTrXddM6jhlWBC8tO7jdxUYHRGifnOuArv+Kt2y JaoSjY+cW5Nd+wTHzv69fbinCtck2tzelv8UtQ7uXxfKrMFsrR+PvcirxaeT k7Vt6rVYGfir7IWnz9A5uuyPrLd1WCEcveRlI8BXGqti0my6cM1ScyOxuhBF nKaE+7p81Grt9AgWCtGP8QjnXvGR6f1HZknpIE79nGc7w+nGQybhuaqxQ1gS IRdoZdODk3onWxb6DuOtgMjnvi09yDXebrXMQYTFTot/NtvWix8ztGzqTcSo lXU6cfvtXgx8l/HDB1kRBDXM3hkVt+POP5uezHUMgWNwQtWt5624bKxigX3Z IGgbqbDcr7eg5X23gMhcIeihgZObTRP6cHZ5ueUKwPjOxV3yDxqQ+Q/DCJey ARi7kVh/ppiLbUaHY5j8fmBydkaqXn6CwZ0a/dOK/cC60hdQ7FSGXKdpvzLe E0i+7KMw7dQHW4+Ov93XWAFxu18dOqE4AFMpBjHOumWQb7/mp3I/AUSn+MWx WSXAPLzegjkohKld6SfN+EXw7qhuctDeIXCXUTr9/vs8uDTDCmHxh6G/0XLC oCgL0kKnnF1+E4OUuaW69XgGlDbb2L4XSaCBY88d4w+BcrxZ+HllAbqUlWv0 7BuECIsd4bNXBKhgaRVp3yUAtdSGpPdSAULUSLbejgFIf+0bZWIjxKnMZqOU iD5YsIDjGhAmRM0+1X+6+naD8u6S1ekPhCif067vad8JRVcPBcW2C/FvzFx2 wqo2SMqrMrAYEOIP5Iwx9KxG7sdser82eR7K0ufJ3vz8PvwgR95nTebBODqP CpkXZem8rmQfPEf34ZF98UMc2Veb9A86tAdH0gsA7cWR9AS5tKfjpDcwoL3x SI+wgPboTnoFf9prKekZrGnPU6R38KC9Uw9gHfWAegEnqRfUE1hBPaHegJh6 40jncaQeGdN5ralXxnSfjxnEMwbdt516x3NpXST3vBL+8jzfdurNKHirLI0d O1UDyyu2CX4RjYBdyL6ou+J6YF+T/874mQQG9V4PdH3Ngz9/S1iZnymGYHuZ WZZ6M8ge7U+46COCrYudS63ftEBh1pCfm+EwFJgLcvvvtQJL8otQbmAQ3IbZ arK726FHOpNnFiaEjVNJ9baVw6DtZTTZWxEKPRPdXpkhIuAlvXXTvJaGJtNr NXkmYuCe8jMZSbiLG6cl33g1iiGNxW9y0kYsXDG4RMNVArP5CUfenajG5NT2 42dfSMD0pVBB4F2PRReszV3Wj8CvShO5BY94yJiVizh2dQQuc64mvmxswX7S AxbRHipIL5hKe7EiPWEw7UlMesPXtDfaIyp+6ZH0il96dSQ9YyztmfaOqbT3 EOIBStnEgy7iBYpvEi8WEU+wknpygniDCtSbTcQjVKUeaROvcCH1yoV4hmbU s/PEOzxIvTvnEPV7qrsEv7mgFOwY24XrO7hlFtViLOj2WbvBohMr9+tmPF4h xmSYTA6eaMcrt0qEMf4iZHN09vWUtuG/197vVqsaxtlNHvHKMa2ofZi9IZs5 jJ72Dp7lgS/worxSQ/W2IYxmy6fE+7fgh/FKff7lQeSWpK9fHdqMbU0dXO3e 5vl9dj4MGriH0wc2+unO77HyyP3sJb/fRbveaZUR20ZkfFwoI2NVgOwQWKzy vh55+ZEZurwc1DpmOnonhou8JKHRbDUHhYnxO58tq0bW5vjwix7pyPZdneb/ r8fzvzN1Pil7U9B7+38Vg+b/P9GRp67r2SZgHfVgsj1WIiviozP1QhrmKpGX duFX1JORGo9nasu70JJ6w9XSFqae6MRJ4h8ypoq3fj3agWrUK+n2mP+Uh3Ug 44tn/aZf8R07UIN615HhnxO+oQMNqIdietakXpbS+/Wopwr25HkKxD/Qou+z oR4P0nlUqdfyXDKvG/VcI5zs00K91+wg+87OfO4Bd9Me8kgvaEB7SSQ9oWCc 9JRLesM7tDcW6REVaI+rSK/Ior22kZ4x7TrpmUV6R3cf0rsj8QCHqQcZxAvc TL2wIJ5gKfXEj3iDTOrNC+IRRlOPVhKvMIJ6ZUc8Qx3qWQHxDh9Q7/4HvCaR vw== "], { {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[Medium], ArrowBox[ BezierCurveBox[{1, {-0.16444074718311624`, 0.49999999999999967`}, 3}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{1, {-0.3507923283006618, -0.3924098644778737}, 4}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{2, {0.18635158111754768`, 0.10759013552212278`}, 3}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{2, {-1.8505415028554895`*^-15, -0.7848197289557458}, 4}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{3, {0.16444074718311655`, 0.5000000000000007}, 1}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{3, {0.6796738226668931, 0.39240986447787535`}, 2}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{3, {-0.18635158111754535`, 0.10759013552212827`}, 4}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{4, {-0.5152330754837754, -0.10759013552212586`}, 1}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{4, {-4.742012601067197*^-15, -0.2151802710442545}, 2}], 0.020399597244776413`], ArrowBox[ BezierCurveBox[{4, {-0.6796738226668936, 0.3924098644778727}, 3}], 0.020399597244776413`]}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], DiskBox[1, 0.020399597244776413], DiskBox[2, 0.020399597244776413], DiskBox[3, 0.020399597244776413], DiskBox[4, 0.020399597244776413]}}]], MouseAppearanceTag["NetworkGraphics"]], AllowKernelInitialization->False]], DefaultBaseStyle->"NetworkGraphics", FormatType->TraditionalForm, FrameTicks->None, ImageSize->{89.39999999999998, Automatic}]\), 2, "Out"]
Out[12]=

Scope (5) 

Works with undirected graphs:

In[13]:=
ResourceFunction["RegularGraphQ"][\!\(\* GraphicsBox[ NamespaceBox["NetworkGraphics", DynamicModuleBox[{Typeset`graph = HoldComplete[ Graph[{1, 2, 3, 4}, {Null, SparseArray[ Automatic, {4, 4}, 0, {1, {{0, 3, 6, 9, 12}, {{2}, {3}, {4}, {1}, {3}, {4}, { 1}, {2}, {4}, {1}, {2}, {3}}}, Pattern}]}, {GraphLayout -> "StarEmbedding"}]]}, TagBox[GraphicsGroupBox[ GraphicsComplexBox[{{0., 0.}, { 0.8660254037844389, -0.5000000000000012}, { 1.8369701987210297`*^-16, 1.}, {-0.8660254037844386, -0.49999999999999917`}}, { {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[0.], ArrowBox[{{1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}}, 0.020399597244776413`]}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], DiskBox[1, 0.020399597244776413], DiskBox[2, 0.020399597244776413], DiskBox[3, 0.020399597244776413], DiskBox[4, 0.020399597244776413]}}]], MouseAppearanceTag["NetworkGraphics"]], AllowKernelInitialization->False]], DefaultBaseStyle->"NetworkGraphics", FormatType->TraditionalForm, FrameTicks->None, ImageSize->{89.39999999999998, Automatic}]\)]
Out[13]=
In[14]:=
ResourceFunction["RegularGraphQ"][\!\(\* GraphicsBox[ NamespaceBox["NetworkGraphics", DynamicModuleBox[{Typeset`graph = HoldComplete[ Graph[{1, 2, 3, 4}, {Null, SparseArray[ Automatic, {4, 4}, 0, {1, {{0, 3, 6, 9, 12}, {{2}, {3}, {4}, {1}, {3}, {4}, { 1}, {2}, {4}, {1}, {2}, {3}}}, Pattern}]}, {GraphLayout -> "StarEmbedding"}]]}, TagBox[GraphicsGroupBox[ GraphicsComplexBox[{{0., 0.}, { 0.8660254037844389, -0.5000000000000012}, { 1.8369701987210297`*^-16, 1.}, {-0.8660254037844386, -0.49999999999999917`}}, { {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[0.], ArrowBox[{{1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}}, 0.020399597244776413`]}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], DiskBox[1, 0.020399597244776413], DiskBox[2, 0.020399597244776413], DiskBox[3, 0.020399597244776413], DiskBox[4, 0.020399597244776413]}}]], MouseAppearanceTag["NetworkGraphics"]], AllowKernelInitialization->False]], DefaultBaseStyle->"NetworkGraphics", FormatType->TraditionalForm, FrameTicks->None, ImageSize->{89.39999999999998, Automatic}]\), "In"]
Out[14]=

Directed graphs:

In[15]:=
ResourceFunction["RegularGraphQ"][\!\(\* GraphicsBox[ NamespaceBox["NetworkGraphics", DynamicModuleBox[{Typeset`graph = HoldComplete[ Graph[{2, 1, 4, 3}, {{{1, 2}, {3, 2}, {4, 1}, {1, 3}, {4, 3}, {1, 4}, {2, 4}, {1, 1}}, Null}]]}, TagBox[GraphicsGroupBox[GraphicsComplexBox[CompressedData[" 1:eJxFjnsw2wcAx9NdpTOPOI5LV1dC9aHrZkHWkt5XKdNDq7rSOW3RmrQz4lHG bGUebayMtqMTFFNSWuo8G2l+IlUN1car1U28E4kYQRzV7az7Y7fv3ec+d5+/ vrTQKL+w90gkkvM7/rXvSOLAumcBKBeog15JarA3rgemf6+GQCa5BfEsSP/t VmeF0jUf/QmRzrWi/zs1oWCoxu8mnLKd5ZzzapQMj3bsFv5GHLdw8Gszn4Xi IqvtGrWN2Bwt/uIzlgre3k6PydwnxO6zdlXfnlTBdqt6ojfkBeFiZkonKVQo ZlVS6PkDRDCz+COGoRpk40qHr+6/JNpdvtxzqnkO2TsPNum3DBNVyymrwYJ5 HJ2O0vhwXhPHwp25Id9pUOLTm+Jt8prYey32yBh3EVcSArIun3lFRNillmTw lqDJSTityR4k0nPDtz/9aRnzccbkr/+QEtWu9o4R9los3q1abbaREIJonSsb eVqkE0Ve31DbiQCTUYO521pkhdXOh1jfJ87pBIyZBGlR6uAUci4tBsH06m3K nmWMBxbtk8XWoPSS2Sdv1pcQJ9e3OktrhjSHEaS7vojALfcWVuofonL1GLdR pkFy7enuy1atcPaY7bueuIDJHY2eW27Uo+/tI7Uy6E+0iknRensKYefTmSvJ VSPisH+H45oISw8vqes4KihWdvG6+Z0QkK3i3Mkq/CDkdPwVKoHhjTA9doIS DF65uGz+GX5nL7umy2aQ6VtgJd0nRT5V76Bs/wy0/f5pawN92L8pLX6Eo0CF 5UUjKWsAR22MslVSOeJrxGbh6kHYls9tijGUw2drcwNlbBremrWdcbRB8F0P pT7Nl0Nob20amtUPPaq6L/WwAp5RBfrbJ6UAf1wyOKMAfYWU6nHiOeZby5uC U2agSXd5OyfuRkyAh1uPgRLvH+ix8KJ24S53oaX9ZyUCx4Pcs/3EuJp8nqbV UcHc5gR7VCVEYVNcmfJvBcYXbbOEunVgHiGx3Aze/TZu2KCXNsD0VfgEw1oO owf57qNmreAV0cp8XKbRKtrFYSoEiC4RkgzDpjB3yDGIryMCU3ZG+iZvEsG3 T8Y/EokRyhjSzemawAcUmjnnzhOss3mZruQJFG6r8wyvk6CiyTfx19huzGq4 7XkXJqCh7HBrvtkF+otMyYeOk7jHTyb1yR4jov5ZL1N3CiOfVlpm+Hagc++w fZJ8Ci6RzKnqEQIvP/f8xVcyDcski3j/6DY8L7TRP9AoR8SpIWl1SAvW7UQ/ 8u4owD7+cQblQQMiNxuSjYpn8A9ToNi6 "], { {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[Medium], ArrowBox[BezierCurveBox[{1, 8, 11, 13, 19, 21, 24, 1}, SplineDegree->7], 0.010935985290500699`], ArrowBox[{1, 2}, 0.010935985290500699`], ArrowBox[{1, 3}, 0.010935985290500699`], ArrowBox[ BezierCurveBox[{1, {0.5706427649235999, 0.5630960172554803}, 4}], 0.010935985290500699`], ArrowBox[{2, 4}, 0.010935985290500699`], ArrowBox[{3, 2}, 0.010935985290500699`], ArrowBox[ BezierCurveBox[{4, {0.28823921905720024`, 0.2955827187147667}, 1}], 0.010935985290500699`], ArrowBox[{4, 3}, 0.010935985290500699`]}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], DiskBox[1, 0.010935985290500699], DiskBox[2, 0.010935985290500699], DiskBox[3, 0.010935985290500699], DiskBox[4, 0.010935985290500699]}}]], MouseAppearanceTag["NetworkGraphics"]], AllowKernelInitialization->False]], DefaultBaseStyle->"NetworkGraphics", FormatType->TraditionalForm, FrameTicks->None, ImageSize->{102.60000000000008`, Automatic}]\)]
Out[15]=
In[16]:=
ResourceFunction["RegularGraphQ"][\!\(\* GraphicsBox[ NamespaceBox["NetworkGraphics", DynamicModuleBox[{Typeset`graph = HoldComplete[ Graph[{2, 1, 4, 3}, {{{1, 2}, {3, 2}, {4, 1}, {1, 3}, {4, 3}, {1, 4}, {2, 4}, {1, 1}}, Null}]]}, TagBox[GraphicsGroupBox[GraphicsComplexBox[CompressedData[" 1:eJxFjnsw2wcAx9NdpTOPOI5LV1dC9aHrZkHWkt5XKdNDq7rSOW3RmrQz4lHG bGUebayMtqMTFFNSWuo8G2l+IlUN1car1U28E4kYQRzV7az7Y7fv3ec+d5+/ vrTQKL+w90gkkvM7/rXvSOLAumcBKBeog15JarA3rgemf6+GQCa5BfEsSP/t VmeF0jUf/QmRzrWi/zs1oWCoxu8mnLKd5ZzzapQMj3bsFv5GHLdw8Gszn4Xi IqvtGrWN2Bwt/uIzlgre3k6PydwnxO6zdlXfnlTBdqt6ojfkBeFiZkonKVQo ZlVS6PkDRDCz+COGoRpk40qHr+6/JNpdvtxzqnkO2TsPNum3DBNVyymrwYJ5 HJ2O0vhwXhPHwp25Id9pUOLTm+Jt8prYey32yBh3EVcSArIun3lFRNillmTw lqDJSTityR4k0nPDtz/9aRnzccbkr/+QEtWu9o4R9los3q1abbaREIJonSsb eVqkE0Ve31DbiQCTUYO521pkhdXOh1jfJ87pBIyZBGlR6uAUci4tBsH06m3K nmWMBxbtk8XWoPSS2Sdv1pcQJ9e3OktrhjSHEaS7vojALfcWVuofonL1GLdR pkFy7enuy1atcPaY7bueuIDJHY2eW27Uo+/tI7Uy6E+0iknRensKYefTmSvJ VSPisH+H45oISw8vqes4KihWdvG6+Z0QkK3i3Mkq/CDkdPwVKoHhjTA9doIS DF65uGz+GX5nL7umy2aQ6VtgJd0nRT5V76Bs/wy0/f5pawN92L8pLX6Eo0CF 5UUjKWsAR22MslVSOeJrxGbh6kHYls9tijGUw2drcwNlbBremrWdcbRB8F0P pT7Nl0Nob20amtUPPaq6L/WwAp5RBfrbJ6UAf1wyOKMAfYWU6nHiOeZby5uC U2agSXd5OyfuRkyAh1uPgRLvH+ix8KJ24S53oaX9ZyUCx4Pcs/3EuJp8nqbV UcHc5gR7VCVEYVNcmfJvBcYXbbOEunVgHiGx3Aze/TZu2KCXNsD0VfgEw1oO owf57qNmreAV0cp8XKbRKtrFYSoEiC4RkgzDpjB3yDGIryMCU3ZG+iZvEsG3 T8Y/EokRyhjSzemawAcUmjnnzhOss3mZruQJFG6r8wyvk6CiyTfx19huzGq4 7XkXJqCh7HBrvtkF+otMyYeOk7jHTyb1yR4jov5ZL1N3CiOfVlpm+Hagc++w fZJ8Ci6RzKnqEQIvP/f8xVcyDcski3j/6DY8L7TRP9AoR8SpIWl1SAvW7UQ/ 8u4owD7+cQblQQMiNxuSjYpn8A9ToNi6 "], { {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[Medium], ArrowBox[BezierCurveBox[{1, 8, 11, 13, 19, 21, 24, 1}, SplineDegree->7], 0.010935985290500699`], ArrowBox[{1, 2}, 0.010935985290500699`], ArrowBox[{1, 3}, 0.010935985290500699`], ArrowBox[ BezierCurveBox[{1, {0.5706427649235999, 0.5630960172554803}, 4}], 0.010935985290500699`], ArrowBox[{2, 4}, 0.010935985290500699`], ArrowBox[{3, 2}, 0.010935985290500699`], ArrowBox[ BezierCurveBox[{4, {0.28823921905720024`, 0.2955827187147667}, 1}], 0.010935985290500699`], ArrowBox[{4, 3}, 0.010935985290500699`]}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], DiskBox[1, 0.010935985290500699], DiskBox[2, 0.010935985290500699], DiskBox[3, 0.010935985290500699], DiskBox[4, 0.010935985290500699]}}]], MouseAppearanceTag["NetworkGraphics"]], AllowKernelInitialization->False]], DefaultBaseStyle->"NetworkGraphics", FormatType->TraditionalForm, FrameTicks->None, ImageSize->{102.60000000000008`, Automatic}]\), "In"]
Out[16]=

Weighted graphs:

In[17]:=
ResourceFunction["RegularGraphQ"][\!\(\* GraphicsBox[ NamespaceBox["NetworkGraphics", DynamicModuleBox[{Typeset`graph = HoldComplete[ Graph[{1, 2, 3, 4, 5}, {Null, SparseArray[ Automatic, {5, 5}, 0, {1, {{0, 3, 6, 8, 9, 10}, {{2}, {3}, {4}, {2}, {3}, { 5}, {4}, {5}, {5}, {5}}}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1}}]}, {FormatType -> TraditionalForm, GraphLayout -> {"Dimension" -> 2}, VertexLabels -> { Placed[Automatic, Center]}, VertexSize -> {0.25}, VertexStyle -> { GrayLevel[1]}}]]}, TagBox[GraphicsGroupBox[{ {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[0.], ArrowBox[{{0., 0.012484330888018924`}, { 0.011333771416589089`, 1.1666638939968836`}}, 0.10192290483023064`], ArrowBox[{{0., 0.012484330888018924`}, {0.5818822250328072, 0.5841484109973273}}, 0.10192290483023064`], ArrowBox[{{0., 0.012484330888018924`}, {1.1541843168018768`, 0.}}, 0.10192290483023064`], ArrowBox[ BezierCurveBox[{{0.011333771416589089`, 1.1666638939968836`}, {-0.18684105756379346`, 1.0962815719756591`}, {-0.3663390917212296, 1.1988433261781792`}, {-0.4132538528198191, 1.3309407689787274`}, {-0.14439391571122775`, 1.5944610769823941`}, {-0.013264036975934812`, 1.544906217419994}, {0.08567681402759109, 1.3633871669206583`}, {0.011333771416589089`, 1.1666638939968836`}}, SplineDegree->7], 0.10192290483023064`], ArrowBox[{{0.011333771416589089`, 1.1666638939968836`}, { 0.5818822250328072, 0.5841484109973273}}, 0.10192290483023064`], ArrowBox[{{0.011333771416589089`, 1.1666638939968836`}, { 1.1666848480058034`, 1.1548334540590575`}}, 0.10192290483023064`], ArrowBox[{{0.5818822250328072, 0.5841484109973273}, { 1.1541843168018768`, 0.}}, 0.10192290483023064`], ArrowBox[{{0.5818822250328072, 0.5841484109973273}, { 1.1666848480058034`, 1.1548334540590575`}}, 0.10192290483023064`], ArrowBox[{{1.1541843168018768`, 0.}, {1.1666848480058034`, 1.1548334540590575`}}, 0.10192290483023064`], ArrowBox[ BezierCurveBox[{{1.1666848480058034`, 1.1548334540590575`}, {1.096428457927411, 1.3530529650328658`}, {1.1990740340904533`, 1.532488387080747}, {1.3311868766939918`, 1.579333895788655}, {1.5945558474459913`, 1.3103582119248316`}, {1.5449381846459758`, 1.1792613301726174`}, {1.3633806566239384`, 1.0804177719107293`}, {1.1666848480058034`, 1.1548334540590575`}}, SplineDegree->7], 0.10192290483023064`]}, {GrayLevel[1], EdgeForm[{GrayLevel[0], Opacity[ 0.7]}], { DiskBox[{0., 0.012484330888018924`}, 0.10192290483023064], InsetBox["1", {0., 0.012484330888018924}, BaseStyle->"Graphics"]}, { DiskBox[{0.011333771416589089`, 1.1666638939968836`}, 0.10192290483023064], InsetBox["2", {0.011333771416589089, 1.1666638939968836}, BaseStyle->"Graphics"]}, { DiskBox[{0.5818822250328072, 0.5841484109973273}, 0.10192290483023064], InsetBox["3", {0.5818822250328072, 0.5841484109973273}, BaseStyle->"Graphics"]}, { DiskBox[{1.1541843168018768`, 0.}, 0.10192290483023064], InsetBox["4", {1.1541843168018768, 0.}, BaseStyle->"Graphics"]}, { DiskBox[{1.1666848480058034`, 1.1548334540590575`}, 0.10192290483023064], InsetBox["5", {1.1666848480058034, 1.1548334540590575}, BaseStyle->"Graphics"]}}}], MouseAppearanceTag["NetworkGraphics"]], AllowKernelInitialization->False]], DefaultBaseStyle->"NetworkGraphics", FormatType->TraditionalForm, FrameTicks->None, ImageSize->{131.4000000000001, Automatic}]\)]
Out[17]=
In[18]:=
ResourceFunction["RegularGraphQ"][\!\(\* GraphicsBox[ NamespaceBox["NetworkGraphics", DynamicModuleBox[{Typeset`graph = HoldComplete[ Graph[{1, 2, 3, 4, 5}, {Null, SparseArray[ Automatic, {5, 5}, 0, {1, {{0, 3, 6, 8, 9, 10}, {{2}, {3}, {4}, {2}, {3}, { 5}, {4}, {5}, {5}, {5}}}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1}}]}, {EdgeWeight -> {1.2369696639583552`, 4.812258229681952, 8.607929577404715, 7.431845779784997, 8.574488000789195, 8.006160372677755, 2.8301481232102947`, 9.121065878848466, 2.3183507378286023`, 1.7298078679288516`}, FormatType -> TraditionalForm, GraphLayout -> {"Dimension" -> 2}, ImageSize -> {131.4000000000001, Automatic}, VertexLabels -> { Placed[Automatic, Center]}, VertexSize -> {0.25}, VertexStyle -> { GrayLevel[1]}}]]}, TagBox[GraphicsGroupBox[{ {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[0.], ArrowBox[{{0., 0.012484330888018924`}, { 0.011333771416589089`, 1.1666638939968836`}}, 0.10192290483023064`], ArrowBox[{{0., 0.012484330888018924`}, {0.5818822250328072, 0.5841484109973273}}, 0.10192290483023064`], ArrowBox[{{0., 0.012484330888018924`}, {1.1541843168018768`, 0.}}, 0.10192290483023064`], ArrowBox[ BezierCurveBox[{{0.011333771416589089`, 1.1666638939968836`}, {-0.18684105756379346`, 1.0962815719756591`}, {-0.3663390917212296, 1.1988433261781792`}, {-0.4132538528198191, 1.3309407689787274`}, {-0.14439391571122775`, 1.5944610769823941`}, {-0.013264036975934812`, 1.544906217419994}, {0.08567681402759109, 1.3633871669206583`}, {0.011333771416589089`, 1.1666638939968836`}}, SplineDegree->7], 0.10192290483023064`], ArrowBox[{{0.011333771416589089`, 1.1666638939968836`}, { 0.5818822250328072, 0.5841484109973273}}, 0.10192290483023064`], ArrowBox[{{0.011333771416589089`, 1.1666638939968836`}, { 1.1666848480058034`, 1.1548334540590575`}}, 0.10192290483023064`], ArrowBox[{{0.5818822250328072, 0.5841484109973273}, { 1.1541843168018768`, 0.}}, 0.10192290483023064`], ArrowBox[{{0.5818822250328072, 0.5841484109973273}, { 1.1666848480058034`, 1.1548334540590575`}}, 0.10192290483023064`], ArrowBox[{{1.1541843168018768`, 0.}, {1.1666848480058034`, 1.1548334540590575`}}, 0.10192290483023064`], ArrowBox[ BezierCurveBox[{{1.1666848480058034`, 1.1548334540590575`}, {1.096428457927411, 1.3530529650328658`}, {1.1990740340904533`, 1.532488387080747}, {1.3311868766939918`, 1.579333895788655}, {1.5945558474459913`, 1.3103582119248316`}, {1.5449381846459758`, 1.1792613301726174`}, {1.3633806566239384`, 1.0804177719107293`}, {1.1666848480058034`, 1.1548334540590575`}}, SplineDegree->7], 0.10192290483023064`]}, {GrayLevel[1], EdgeForm[{GrayLevel[0], Opacity[ 0.7]}], { DiskBox[{0., 0.012484330888018924`}, 0.10192290483023064], InsetBox["1", {0., 0.012484330888018924}, BaseStyle->"Graphics"]}, { DiskBox[{0.011333771416589089`, 1.1666638939968836`}, 0.10192290483023064], InsetBox["2", {0.011333771416589089, 1.1666638939968836}, BaseStyle->"Graphics"]}, { DiskBox[{0.5818822250328072, 0.5841484109973273}, 0.10192290483023064], InsetBox["3", {0.5818822250328072, 0.5841484109973273}, BaseStyle->"Graphics"]}, { DiskBox[{1.1541843168018768`, 0.}, 0.10192290483023064], InsetBox["4", {1.1541843168018768, 0.}, BaseStyle->"Graphics"]}, { DiskBox[{1.1666848480058034`, 1.1548334540590575`}, 0.10192290483023064], InsetBox["5", {1.1666848480058034, 1.1548334540590575}, BaseStyle->"Graphics"]}}}], MouseAppearanceTag["NetworkGraphics"]], AllowKernelInitialization->False]], DefaultBaseStyle->"NetworkGraphics", FormatType->TraditionalForm, FrameTicks->None, ImageSize->{131.4000000000001, Automatic}]\), "In"]
Out[18]=

Multigraphs:

In[19]:=
ResourceFunction["RegularGraphQ"][\!\(\* GraphicsBox[ NamespaceBox["NetworkGraphics", DynamicModuleBox[{Typeset`graph = HoldComplete[ Graph[{2, 1, 4, 3}, {{{1, 2}, {3, 2}, {4, 1}, {1, 3}, {4, 3}, {1, 4}, {2, 4}, {1, 1}}, Null}]]}, TagBox[GraphicsGroupBox[GraphicsComplexBox[CompressedData[" 1:eJxFjnsw2wcAx9NdpTOPOI5LV1dC9aHrZkHWkt5XKdNDq7rSOW3RmrQz4lHG bGUebayMtqMTFFNSWuo8G2l+IlUN1car1U28E4kYQRzV7az7Y7fv3ec+d5+/ vrTQKL+w90gkkvM7/rXvSOLAumcBKBeog15JarA3rgemf6+GQCa5BfEsSP/t VmeF0jUf/QmRzrWi/zs1oWCoxu8mnLKd5ZzzapQMj3bsFv5GHLdw8Gszn4Xi IqvtGrWN2Bwt/uIzlgre3k6PydwnxO6zdlXfnlTBdqt6ojfkBeFiZkonKVQo ZlVS6PkDRDCz+COGoRpk40qHr+6/JNpdvtxzqnkO2TsPNum3DBNVyymrwYJ5 HJ2O0vhwXhPHwp25Id9pUOLTm+Jt8prYey32yBh3EVcSArIun3lFRNillmTw lqDJSTityR4k0nPDtz/9aRnzccbkr/+QEtWu9o4R9los3q1abbaREIJonSsb eVqkE0Ve31DbiQCTUYO521pkhdXOh1jfJ87pBIyZBGlR6uAUci4tBsH06m3K nmWMBxbtk8XWoPSS2Sdv1pcQJ9e3OktrhjSHEaS7vojALfcWVuofonL1GLdR pkFy7enuy1atcPaY7bueuIDJHY2eW27Uo+/tI7Uy6E+0iknRensKYefTmSvJ VSPisH+H45oISw8vqes4KihWdvG6+Z0QkK3i3Mkq/CDkdPwVKoHhjTA9doIS DF65uGz+GX5nL7umy2aQ6VtgJd0nRT5V76Bs/wy0/f5pawN92L8pLX6Eo0CF 5UUjKWsAR22MslVSOeJrxGbh6kHYls9tijGUw2drcwNlbBremrWdcbRB8F0P pT7Nl0Nob20amtUPPaq6L/WwAp5RBfrbJ6UAf1wyOKMAfYWU6nHiOeZby5uC U2agSXd5OyfuRkyAh1uPgRLvH+ix8KJ24S53oaX9ZyUCx4Pcs/3EuJp8nqbV UcHc5gR7VCVEYVNcmfJvBcYXbbOEunVgHiGx3Aze/TZu2KCXNsD0VfgEw1oO owf57qNmreAV0cp8XKbRKtrFYSoEiC4RkgzDpjB3yDGIryMCU3ZG+iZvEsG3 T8Y/EokRyhjSzemawAcUmjnnzhOss3mZruQJFG6r8wyvk6CiyTfx19huzGq4 7XkXJqCh7HBrvtkF+otMyYeOk7jHTyb1yR4jov5ZL1N3CiOfVlpm+Hagc++w fZJ8Ci6RzKnqEQIvP/f8xVcyDcski3j/6DY8L7TRP9AoR8SpIWl1SAvW7UQ/ 8u4owD7+cQblQQMiNxuSjYpn8A9ToNi6 "], { {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[Medium], ArrowBox[BezierCurveBox[{1, 8, 11, 13, 19, 21, 24, 1}, SplineDegree->7], 0.010935985290500699`], ArrowBox[{1, 2}, 0.010935985290500699`], ArrowBox[{1, 3}, 0.010935985290500699`], ArrowBox[ BezierCurveBox[{1, {0.5706427649235999, 0.5630960172554803}, 4}], 0.010935985290500699`], ArrowBox[{2, 4}, 0.010935985290500699`], ArrowBox[{3, 2}, 0.010935985290500699`], ArrowBox[ BezierCurveBox[{4, {0.28823921905720024`, 0.2955827187147667}, 1}], 0.010935985290500699`], ArrowBox[{4, 3}, 0.010935985290500699`]}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], DiskBox[1, 0.010935985290500699], DiskBox[2, 0.010935985290500699], DiskBox[3, 0.010935985290500699], DiskBox[4, 0.010935985290500699]}}]], MouseAppearanceTag["NetworkGraphics"]], AllowKernelInitialization->False]], DefaultBaseStyle->"NetworkGraphics", FormatType->TraditionalForm, FrameTicks->None, ImageSize->{102.60000000000008`, Automatic}]\)]
Out[19]=
In[20]:=
ResourceFunction["RegularGraphQ"][\!\(\* GraphicsBox[ NamespaceBox["NetworkGraphics", DynamicModuleBox[{Typeset`graph = HoldComplete[ Graph[{2, 1, 4, 3}, {{{1, 2}, {3, 2}, {4, 1}, {1, 3}, {4, 3}, {1, 4}, {2, 4}, {1, 1}}, Null}]]}, TagBox[GraphicsGroupBox[GraphicsComplexBox[CompressedData[" 1:eJxFjnsw2wcAx9NdpTOPOI5LV1dC9aHrZkHWkt5XKdNDq7rSOW3RmrQz4lHG bGUebayMtqMTFFNSWuo8G2l+IlUN1car1U28E4kYQRzV7az7Y7fv3ec+d5+/ vrTQKL+w90gkkvM7/rXvSOLAumcBKBeog15JarA3rgemf6+GQCa5BfEsSP/t VmeF0jUf/QmRzrWi/zs1oWCoxu8mnLKd5ZzzapQMj3bsFv5GHLdw8Gszn4Xi IqvtGrWN2Bwt/uIzlgre3k6PydwnxO6zdlXfnlTBdqt6ojfkBeFiZkonKVQo ZlVS6PkDRDCz+COGoRpk40qHr+6/JNpdvtxzqnkO2TsPNum3DBNVyymrwYJ5 HJ2O0vhwXhPHwp25Id9pUOLTm+Jt8prYey32yBh3EVcSArIun3lFRNillmTw lqDJSTityR4k0nPDtz/9aRnzccbkr/+QEtWu9o4R9los3q1abbaREIJonSsb eVqkE0Ve31DbiQCTUYO521pkhdXOh1jfJ87pBIyZBGlR6uAUci4tBsH06m3K nmWMBxbtk8XWoPSS2Sdv1pcQJ9e3OktrhjSHEaS7vojALfcWVuofonL1GLdR pkFy7enuy1atcPaY7bueuIDJHY2eW27Uo+/tI7Uy6E+0iknRensKYefTmSvJ VSPisH+H45oISw8vqes4KihWdvG6+Z0QkK3i3Mkq/CDkdPwVKoHhjTA9doIS DF65uGz+GX5nL7umy2aQ6VtgJd0nRT5V76Bs/wy0/f5pawN92L8pLX6Eo0CF 5UUjKWsAR22MslVSOeJrxGbh6kHYls9tijGUw2drcwNlbBremrWdcbRB8F0P pT7Nl0Nob20amtUPPaq6L/WwAp5RBfrbJ6UAf1wyOKMAfYWU6nHiOeZby5uC U2agSXd5OyfuRkyAh1uPgRLvH+ix8KJ24S53oaX9ZyUCx4Pcs/3EuJp8nqbV UcHc5gR7VCVEYVNcmfJvBcYXbbOEunVgHiGx3Aze/TZu2KCXNsD0VfgEw1oO owf57qNmreAV0cp8XKbRKtrFYSoEiC4RkgzDpjB3yDGIryMCU3ZG+iZvEsG3 T8Y/EokRyhjSzemawAcUmjnnzhOss3mZruQJFG6r8wyvk6CiyTfx19huzGq4 7XkXJqCh7HBrvtkF+otMyYeOk7jHTyb1yR4jov5ZL1N3CiOfVlpm+Hagc++w fZJ8Ci6RzKnqEQIvP/f8xVcyDcski3j/6DY8L7TRP9AoR8SpIWl1SAvW7UQ/ 8u4owD7+cQblQQMiNxuSjYpn8A9ToNi6 "], { {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[Medium], ArrowBox[BezierCurveBox[{1, 8, 11, 13, 19, 21, 24, 1}, SplineDegree->7], 0.010935985290500699`], ArrowBox[{1, 2}, 0.010935985290500699`], ArrowBox[{1, 3}, 0.010935985290500699`], ArrowBox[ BezierCurveBox[{1, {0.5706427649235999, 0.5630960172554803}, 4}], 0.010935985290500699`], ArrowBox[{2, 4}, 0.010935985290500699`], ArrowBox[{3, 2}, 0.010935985290500699`], ArrowBox[ BezierCurveBox[{4, {0.28823921905720024`, 0.2955827187147667}, 1}], 0.010935985290500699`], ArrowBox[{4, 3}, 0.010935985290500699`]}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], DiskBox[1, 0.010935985290500699], DiskBox[2, 0.010935985290500699], DiskBox[3, 0.010935985290500699], DiskBox[4, 0.010935985290500699]}}]], MouseAppearanceTag["NetworkGraphics"]], AllowKernelInitialization->False]], DefaultBaseStyle->"NetworkGraphics", FormatType->TraditionalForm, FrameTicks->None, ImageSize->{102.60000000000008`, Automatic}]\), "In"]
Out[20]=

Mixed graphs:

In[21]:=
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Out[21]=
In[22]:=
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Out[22]=

Requirements

Wolfram Language 13.0 (December 2021) or above

Version History

  • 1.0.0 – 01 November 2024

Related Resources

License Information