Function Repository Resource:

Girth

Source Notebook

Return the girth of a graph

Contributed by: Alejandra Ortiz Duran

ResourceFunction["Girth"][g]

returns the girth of the graph g.

Details

ResourceFunction["Girth"]

The girth of a graph is the length of its shortest cycle, or infinity if the graph is acyclic.

Girth works with undirected graphs, directed graphs, weighted graphs and multigraphs.

Examples

Basic Examples (1)

Find the girth of a graph:

In[1]:=

$ResourceFunction["Girth"][\!\(\* GraphicsBox[ NamespaceBox["NetworkGraphics", DynamicModuleBox[{Typeset`graph = HoldComplete[ Graph[{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, {Null, SparseArray[ Automatic, {10, 10}, 0, {1, {{0, 6, 11, 16, 25, 31, 36, 42, 49, 54, 60}, {{3}, { 4}, {7}, {8}, {9}, {10}, {3}, {4}, {5}, {6}, {8}, {1}, { 2}, {4}, {5}, {7}, {1}, {2}, {3}, {5}, {6}, {7}, {8}, { 9}, {10}, {2}, {3}, {4}, {6}, {8}, {10}, {2}, {4}, {5}, { 7}, {9}, {1}, {3}, {4}, {6}, {8}, {10}, {1}, {2}, {4}, { 5}, {7}, {9}, {10}, {1}, {4}, {6}, {8}, {10}, {1}, {4}, { 5}, {7}, {8}, {9}}}, Pattern}]}]]}, TagBox[GraphicsGroupBox[ GraphicsComplexBox[{{0., 0.6239426544502702}, { 2.151849427687056, 0.8663508441168547}, {1.1984941271761043`, 0.}, {1.1623140959702059`, 1.0384744365678864`}, { 1.7684823629469641`, 0.4011301459628184}, { 1.5536811184444583`, 1.6745491724169945`}, { 0.5126456674491531, 1.0340214448551166`}, { 0.9865291655352957, 0.6073513293633286}, {0.380334769863935, 1.5799792652846167`}, {0.4479019364967143, 0.28120570767242825`}}, { {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[0.], ArrowBox[{{1, 3}, {1, 4}, {1, 7}, {1, 8}, {1, 9}, {1, 10}, {2, 3}, {2, 4}, {2, 5}, {2, 6}, {2, 8}, {3, 4}, {3, 5}, {3, 7}, {4, 5}, {4, 6}, {4, 7}, {4, 8}, {4, 9}, {4, 10}, {5, 6}, {5, 8}, {5, 10}, {6, 7}, {6, 9}, {7, 8}, {7, 10}, {8, 9}, {8, 10}, {9, 10}}, 0.02383175640649393]}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], DiskBox[1, 0.02383175640649393], DiskBox[2, 0.02383175640649393], DiskBox[3, 0.02383175640649393], DiskBox[4, 0.02383175640649393], DiskBox[5, 0.02383175640649393], DiskBox[6, 0.02383175640649393], DiskBox[7, 0.02383175640649393], DiskBox[8, 0.02383175640649393], DiskBox[9, 0.02383175640649393], DiskBox[10, 0.02383175640649393]}}]], MouseAppearanceTag["NetworkGraphics"]], AllowKernelInitialization->False]], DefaultBaseStyle->"NetworkGraphics", FormatType->TraditionalForm, FrameTicks->None]\)]$

Out[1]=

Scope (6)

Works with undirected graphs:

In[2]:=

$ResourceFunction["Girth"][\!\(\* GraphicsBox[ NamespaceBox["NetworkGraphics", DynamicModuleBox[{Typeset`graph = HoldComplete[ Graph[{1, 2, 3, 4, 5, 6}, {Null, {{1, 2}, {1, 5}, {2, 3}, {3, 4}, {4, 5}, {3, 6}, { 4, 6}}}, {VertexShapeFunction -> {"Name"}}]], Typeset`boxes, Typeset`boxes$s2d = GraphicsGroupBox[{{ Directive[ Hue[0.6, 0.2, 0.8], EdgeForm[ Directive[ GrayLevel[0], Opacity[0.7]]]], TagBox[ InsetBox[ BoxData[ FormBox[ PaneBox["1", Alignment -> Center, ImageMargins -> 2], TraditionalForm]], {2.411646273071402, 0.8121065824762125}, BaseStyle -> "Graphics"], "DynamicName", BoxID -> "VertexID$1"], TagBox[ InsetBox[ BoxData[ FormBox[ PaneBox["2", Alignment -> Center, ImageMargins -> 2], TraditionalForm]], {1.7309526984773034`, 1.6154665631452636`}, BaseStyle -> "Graphics"], "DynamicName", BoxID -> "VertexID$2"], TagBox[ InsetBox[ BoxData[ FormBox[ PaneBox["3", Alignment -> Center, ImageMargins -> 2], TraditionalForm]], {0.7647124196053587, 1.3112048683327449`}, BaseStyle -> "Graphics"], "DynamicName", BoxID -> "VertexID$3"], TagBox[ InsetBox[ BoxData[ FormBox[ PaneBox["4", Alignment -> Center, ImageMargins -> 2], TraditionalForm]], {0.7596612845255981, 0.29540037412003695`}, BaseStyle -> "Graphics"], "DynamicName", BoxID -> "VertexID$4"], TagBox[ InsetBox[ BoxData[ FormBox[ PaneBox["5", Alignment -> Center, ImageMargins -> 2], TraditionalForm]], {1.733605567918051, 0.}, BaseStyle -> "Graphics"], "DynamicName", BoxID -> "VertexID$5"], TagBox[ InsetBox[ BoxData[ FormBox[ PaneBox["6", Alignment -> Center, ImageMargins -> 2], TraditionalForm]], {0., 0.8156390434469147}, BaseStyle -> "Graphics"], "DynamicName", BoxID -> "VertexID$6"]}, { Directive[ Opacity[0.7], Hue[0.6, 0.7, 0.5]], LineBox[{{ DynamicLocation["VertexID$1", Automatic, Center], DynamicLocation["VertexID$2", Automatic, Center]}, { DynamicLocation["VertexID$1", Automatic, Center], DynamicLocation["VertexID$5", Automatic, Center]}, { DynamicLocation["VertexID$2", Automatic, Center], DynamicLocation["VertexID$3", Automatic, Center]}, { DynamicLocation["VertexID$3", Automatic, Center], DynamicLocation["VertexID$4", Automatic, Center]}, { DynamicLocation["VertexID$3", Automatic, Center], DynamicLocation["VertexID$6", Automatic, Center]}, { DynamicLocation["VertexID$4", Automatic, Center], DynamicLocation["VertexID$5", Automatic, Center]}, { DynamicLocation["VertexID$4", Automatic, Center], DynamicLocation["VertexID$6", Automatic, Center]}}]}}], Typeset`data}, TagBox[ DynamicBox[GraphComputation`NetworkGraphicsBox[ 2, Typeset`graph, Typeset`boxes], {CachedValue :> Typeset`boxes, SingleEvaluation -> True, SynchronousUpdating -> False, TrackedSymbols :> {}}, ImageSizeCache->{{0., 98.99999999999999}, {-40.72058321019611, 34.1073019601961}}], MouseAppearanceTag["NetworkGraphics"]], AllowKernelInitialization->False, UnsavedVariables:>{Typeset`data}]], DefaultBaseStyle->{"NetworkGraphics", FrontEnd`GraphicsHighlightColor -> Hue[0.8, 1., 0.6]}, FrameTicks->None, ImageMargins->0.]\)]$

Out[2]=

Directed graphs:

In[3]:=

$ResourceFunction["Girth"][\!\(\* GraphicsBox[ NamespaceBox["NetworkGraphics", DynamicModuleBox[{Typeset`graph = HoldComplete[ Graph[{1, 2, 5, 3, 4, 6}, {{{1, 2}, {1, 3}, {2, 4}, {4, 5}, {5, 3}, {4, 6}, {5, 6}, {6, 4}, {6, 5}, {5, 4}}, Null}, {EdgeStyle -> { Arrowheads[0.08]}, PerformanceGoal -> "Quality", VertexCoordinates -> {{2.5250697157998934`, 0.7575043438370492}, {1.8686026289525572`, 1.514280326539965}, {1.8692822428969822`, 0.}, { 1.208492062014356, 1.2147185278284447`}, {1.208227180246839, 0.2994845613355314}, {0., 0.7572063797178915}}, VertexShapeFunction -> {"Name"}}]], Typeset`boxes, Typeset`boxes$s2d = GraphicsGroupBox[{{ Arrowheads[0.03102368872258745], Directive[ Opacity[0.7], Hue[0.6, 0.7, 0.5]], Arrowheads[0.08], ArrowBox[{ DynamicLocation["VertexID$1", Automatic, Center], DynamicLocation["VertexID$2", Automatic, Center]}], ArrowBox[{ DynamicLocation["VertexID$1", Automatic, Center], DynamicLocation["VertexID$3", Automatic, Center]}], ArrowBox[{ DynamicLocation["VertexID$2", Automatic, Center], DynamicLocation["VertexID$4", Automatic, Center]}], ArrowBox[ BezierCurveBox[{ DynamicLocation["VertexID$4", Automatic, Center], { 1.3344848840593007`, 0.7570650421314713}, DynamicLocation["VertexID$5", Automatic, Center]}]], ArrowBox[ BezierCurveBox[{ DynamicLocation["VertexID$4", Automatic, Center], {0.6672942154999746, 0.8194242956092235}, DynamicLocation["VertexID$6", Automatic, Center]}]], ArrowBox[{ DynamicLocation["VertexID$5", Automatic, Center], DynamicLocation["VertexID$3", Automatic, Center]}], ArrowBox[ BezierCurveBox[{ DynamicLocation["VertexID$5", Automatic, Center], { 1.0822343582018943`, 0.757138047032505}, DynamicLocation["VertexID$4", Automatic, Center]}]], ArrowBox[ BezierCurveBox[{ DynamicLocation["VertexID$5", Automatic, Center], {0.5410365116875129, 0.36184381481328354`}, DynamicLocation["VertexID$6", Automatic, Center]}]], ArrowBox[ BezierCurveBox[{ DynamicLocation["VertexID$6", Automatic, Center], {0.5411978465143815, 1.152500611937113}, DynamicLocation["VertexID$4", Automatic, Center]}]], ArrowBox[ BezierCurveBox[{ DynamicLocation["VertexID$6", Automatic, Center], {0.6671906685593262, 0.6948471262401396}, DynamicLocation["VertexID$5", Automatic, Center]}]]}, { Directive[ Hue[0.6, 0.2, 0.8], EdgeForm[ Directive[ GrayLevel[0], Opacity[0.7]]]], TagBox[ InsetBox[ BoxData[ FormBox[ PaneBox["1", Alignment -> Center, ImageMargins -> 2], TraditionalForm]], {2.5250697157998934`, 0.7575043438370492}, BaseStyle -> "Graphics"], "DynamicName", BoxID -> "VertexID$1"], TagBox[ InsetBox[ BoxData[ FormBox[ PaneBox["2", Alignment -> Center, ImageMargins -> 2], TraditionalForm]], {1.8686026289525572`, 1.514280326539965}, BaseStyle -> "Graphics"], "DynamicName", BoxID -> "VertexID$2"], TagBox[ InsetBox[ BoxData[ FormBox[ PaneBox["5", Alignment -> Center, ImageMargins -> 2], TraditionalForm]], {1.8692822428969822`, 0.}, BaseStyle -> "Graphics"], "DynamicName", BoxID -> "VertexID$3"], TagBox[ InsetBox[ BoxData[ FormBox[ PaneBox["3", Alignment -> Center, ImageMargins -> 2], TraditionalForm]], {1.208492062014356, 1.2147185278284447`}, BaseStyle -> "Graphics"], "DynamicName", BoxID -> "VertexID$4"], TagBox[ InsetBox[ BoxData[ FormBox[ PaneBox["4", Alignment -> Center, ImageMargins -> 2], TraditionalForm]], {1.208227180246839, 0.2994845613355314}, BaseStyle -> "Graphics"], "DynamicName", BoxID -> "VertexID$5"], TagBox[ InsetBox[ BoxData[ FormBox[ PaneBox["6", Alignment -> Center, ImageMargins -> 2], TraditionalForm]], {0., 0.7572063797178915}, BaseStyle -> "Graphics"], "DynamicName", BoxID -> "VertexID$6"]}}], $CellContext`flag}, TagBox[ DynamicBox[GraphComputation`NetworkGraphicsBox[ 3, Typeset`graph, Typeset`boxes, $CellContext`flag], {CachedValue :> Typeset`boxes, SingleEvaluation -> True, SynchronousUpdating -> False, TrackedSymbols :> {$CellContext`flag}}, ImageSizeCache->{{8.881784197001252*^-16, 99.}, {-37.605359863567244`, 30.99207861356723}}], MouseAppearanceTag["NetworkGraphics"]], AllowKernelInitialization->False, UnsavedVariables:>{$CellContext`flag}]], DefaultBaseStyle->{"NetworkGraphics", FrontEnd`GraphicsHighlightColor -> Hue[0.8, 1., 0.6]}, FrameTicks->None, GridLinesStyle->Directive[ GrayLevel[0.5, 0.4]]]\)]$

Out[3]=

Weighted graphs:

In[4]:=

$ResourceFunction["Girth"][\!\(\* GraphicsBox[ NamespaceBox["NetworkGraphics", DynamicModuleBox[{Typeset`graph = HoldComplete[ Graph[{1, 2, 5, 3, 4, 6}, {Null, {{1, 2}, {1, 3}, {2, 4}, {4, 5}, {5, 3}, {4, 6}, { 5, 6}}}, {VertexLabels -> {6 -> Placed[4.1, Before], 3 -> Placed[1.9, Above], 5 -> Placed[3.1, Below], 4 -> Placed[2.1, Below], 2 -> Placed[10, Above], 1 -> Placed[1.6, After]}, VertexWeight -> {1.6, 10, 1.9, 2.1, 3.1, 4.1}, VertexCoordinates -> {{1.9595652573438145`, 0.5880825319731845}, {1.4502332118640586`, 1.1759717047601015`}, {1.4506626970033527`, 0.}, { 0.6271580681226379, 0.9434230409725781}, { 0.6269943909097138, 0.23230866903609504`}, {0., 0.5879767003984426}}}]]}, TagBox[GraphicsGroupBox[{ {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[0.], ArrowBox[{{{1.9595652573438145`, 0.5880825319731845}, { 1.4502332118640586`, 1.1759717047601015`}}, {{ 1.9595652573438145`, 0.5880825319731845}, { 1.4506626970033527`, 0.}}, {{1.4502332118640586`, 1.1759717047601015`}, {0.6271580681226379, 0.9434230409725781}}, {{1.4506626970033527`, 0.}, { 0.6269943909097138, 0.23230866903609504`}}, {{ 0.6271580681226379, 0.9434230409725781}, { 0.6269943909097138, 0.23230866903609504`}}, {{ 0.6271580681226379, 0.9434230409725781}, {0., 0.5879767003984426}}, {{0.6269943909097138, 0.23230866903609504`}, {0., 0.5879767003984426}}}, 0.022282533574036062`]}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[ 0.7]}], { DiskBox[{1.9595652573438145`, 0.5880825319731845}, 0.022282533574036062], InsetBox["1.6`", Offset[{2, 0}, {1.9818477909178505, 0.5880825319731845}], ImageScaled[{0, 0.5}], BaseStyle->"Graphics"]}, { DiskBox[{1.4502332118640586`, 1.1759717047601015`}, 0.022282533574036062], InsetBox["10", Offset[{0, 2}, {1.4502332118640586, 1.1982542383341375}], ImageScaled[{0.5, 0}], BaseStyle->"Graphics"]}, { DiskBox[{1.4506626970033527`, 0.}, 0.022282533574036062], InsetBox["3.1`", Offset[{0, -2}, {1.4506626970033527, -0.022282533574036062}], ImageScaled[{0.5, 1}], BaseStyle->"Graphics"]}, { DiskBox[{0.6271580681226379, 0.9434230409725781}, 0.022282533574036062], InsetBox["1.9`", Offset[{0, 2}, {0.6271580681226379, 0.9657055745466142}], ImageScaled[{0.5, 0}], BaseStyle->"Graphics"]}, { DiskBox[{0.6269943909097138, 0.23230866903609504`}, 0.022282533574036062], InsetBox["2.1`", Offset[{0, -2}, {0.6269943909097138, 0.21002613546205898}], ImageScaled[{0.5, 1}], BaseStyle->"Graphics"]}, { DiskBox[{0., 0.5879767003984426}, 0.022282533574036062], InsetBox["4.1`", Offset[{-2, 0}, {-0.022282533574036062, 0.5879767003984426}], ImageScaled[{1, 0.5}], BaseStyle->"Graphics"]}}}], MouseAppearanceTag["NetworkGraphics"]], AllowKernelInitialization->False]], DefaultBaseStyle->{"NetworkGraphics", FrontEnd`GraphicsHighlightColor -> Hue[0.8, 1., 0.6]}, FrameTicks->None, GridLinesStyle->Directive[ GrayLevel[0.5, 0.4]], ImagePadding->15]\)]$

Out[4]=

Multigraphs:

In[5]:=

$ResourceFunction["Girth"][\!\(\* GraphicsBox[ NamespaceBox["NetworkGraphics", DynamicModuleBox[{Typeset`graph = HoldComplete[ Graph[{1, 2, 5, 3, 4, 6}, {Null, {{1, 2}, {1, 2}, {1, 2}, {1, 3}, {2, 4}, {4, 5}, { 4, 5}, {5, 3}, {4, 6}, {5, 6}}}, {PerformanceGoal -> "Quality", VertexShapeFunction -> {"Name"}}]], Typeset`boxes, Typeset`boxes$s2d = GraphicsGroupBox[{{ Directive[ Opacity[0.7], Hue[0.6, 0.7, 0.5]], FontFamily -> "Arial", BezierCurveBox[{ DynamicLocation["VertexID$1", Automatic, Center], {2.091759444786367, 1.0457453609716316`}, DynamicLocation["VertexID$2", Automatic, Center]}], LineBox[{ DynamicLocation["VertexID$1", Automatic, Center], DynamicLocation["VertexID$2", Automatic, Center]}], BezierCurveBox[{ DynamicLocation["VertexID$1", Automatic, Center], {2.300473686698988, 1.2265700073078933`}, DynamicLocation["VertexID$2", Automatic, Center]}], LineBox[{ DynamicLocation["VertexID$1", Automatic, Center], DynamicLocation["VertexID$3", Automatic, Center]}], LineBox[{ DynamicLocation["VertexID$2", Automatic, Center], DynamicLocation["VertexID$4", Automatic, Center]}], LineBox[{ DynamicLocation["VertexID$3", Automatic, Center], DynamicLocation["VertexID$5", Automatic, Center]}], BezierCurveBox[{ DynamicLocation["VertexID$4", Automatic, Center], {0.9339810990703828, 0.757213318680422}, DynamicLocation["VertexID$5", Automatic, Center]}], BezierCurveBox[{ DynamicLocation["VertexID$4", Automatic, Center], {0.6815190638396575, 0.7572714278734384}, DynamicLocation["VertexID$5", Automatic, Center]}], LineBox[{ DynamicLocation["VertexID$4", Automatic, Center], DynamicLocation["VertexID$6", Automatic, Center]}], LineBox[{ DynamicLocation["VertexID$5", Automatic, Center], DynamicLocation["VertexID$6", Automatic, Center]}]}, { Directive[ Hue[0.6, 0.2, 0.8], EdgeForm[ Directive[ GrayLevel[0], Opacity[0.7]]]], FontFamily -> "Arial", TagBox[ InsetBox[ BoxData[ FormBox[ PaneBox["1", Alignment -> Center, ImageMargins -> 2], TraditionalForm]], {2.524157226398363, 0.7575214794381879}, BaseStyle -> "Graphics"], "DynamicName", BoxID -> "VertexID$1"], TagBox[ InsetBox[ BoxData[ FormBox[ PaneBox["2", Alignment -> Center, ImageMargins -> 2], TraditionalForm]], {1.8680759050869926`, 1.514793888841337}, BaseStyle -> "Graphics"], "DynamicName", BoxID -> "VertexID$2"], TagBox[ InsetBox[ BoxData[ FormBox[ PaneBox["5", Alignment -> Center, ImageMargins -> 2], TraditionalForm]], {1.868629133928909, 0.}, BaseStyle -> "Graphics"], "DynamicName", BoxID -> "VertexID$3"], TagBox[ InsetBox[ BoxData[ FormBox[ PaneBox["3", Alignment -> Center, ImageMargins -> 2], TraditionalForm]], {0.8078554994854354, 1.2152430634790714`}, BaseStyle -> "Graphics"], "DynamicName", BoxID -> "VertexID$4"], TagBox[ InsetBox[ BoxData[ FormBox[ PaneBox["4", Alignment -> Center, ImageMargins -> 2], TraditionalForm]], {0.8076446634246047, 0.2992416830747889}, BaseStyle -> "Graphics"], "DynamicName", BoxID -> "VertexID$5"], TagBox[ InsetBox[ BoxData[ FormBox[ PaneBox["6", Alignment -> Center, ImageMargins -> 2], TraditionalForm]], {0., 0.757385155560652}, BaseStyle -> "Graphics"], "DynamicName", BoxID -> "VertexID$6"]}}], $CellContext`flag}, TagBox[ DynamicBox[GraphComputation`NetworkGraphicsBox[ 3, Typeset`graph, Typeset`boxes, $CellContext`flag], {CachedValue :> Typeset`boxes, SingleEvaluation -> True, SynchronousUpdating -> False, TrackedSymbols :> {$CellContext`flag}}, ImageSizeCache->{{0., 98.99999999999999}, {-37.624019192495915`, 31.01073794249593}}], MouseAppearanceTag["NetworkGraphics"]], AllowKernelInitialization->False, UnsavedVariables:>{$CellContext`flag}]], BaseStyle->(FontFamily -> "Arial"), DefaultBaseStyle->{"NetworkGraphics", FrontEnd`GraphicsHighlightColor -> Hue[0.8, 1., 0.6]}, FrameTicks->None, GridLinesStyle->Directive[ GrayLevel[0.5, 0.4]], LabelStyle->{FontFamily -> "Arial"}]\)]$

Out[5]=

Acyclic graphs have infinite girth:

In[6]:=

$ResourceFunction["Girth"][\!\(\* GraphicsBox[ NamespaceBox["NetworkGraphics", DynamicModuleBox[{Typeset`graph = HoldComplete[ Graph[{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}, {Null, SparseArray[ Automatic, {14, 14}, 0, {1, {{0, 4, 8, 9, 10, 11, 15, 16, 17, 18, 22, 23, 24, 25, 26}, {{2}, {6}, {10}, {14}, {1}, {3}, {4}, {5}, {2}, { 2}, {2}, {1}, {7}, {8}, {9}, {6}, {6}, {6}, {1}, {11}, { 12}, {13}, {10}, {10}, {10}, {1}}}, Pattern}]}, {VertexCoordinates -> {{0, 0}, {1, 0}, {2, 0}, {1, 1}, {1, -1}, { Rational[-1, 2], Rational[-1, 2] 3^Rational[1, 2]}, {-1, -3^Rational[1, 2]}, {Rational[ 1, 2] (-1 - 3^Rational[1, 2]), Rational[1, 2] (1 - 3^Rational[1, 2])}, {Rational[ 1, 2] (-1 + 3^Rational[1, 2]), Rational[1, 2] (-1 - 3^Rational[1, 2])}, { Rational[-1, 2], Rational[1, 2] 3^Rational[1, 2]}, {-1, 3^Rational[1, 2]}, {Rational[ 1, 2] (-1 + 3^Rational[1, 2]), Rational[1, 2] (1 + 3^Rational[1, 2])}, {Rational[ 1, 2] (-1 - 3^Rational[1, 2]), Rational[1, 2] (-1 + 3^Rational[1, 2])}, {-1, 0}}}]]}, TagBox[GraphicsGroupBox[ GraphicsComplexBox[{{0., 0.}, {1., 0.}, {2., 0.}, {1., 1.}, { 1., -1.}, {-0.5, -0.8660254037844386}, {-1., -1.7320508075688772`}, {-1.3660254037844386`, -0.3660254037844386}, { 0.3660254037844386, -1.3660254037844386`}, {-0.5, 0.8660254037844386}, {-1., 1.7320508075688772`}, { 0.3660254037844386, 1.3660254037844386`}, {-1.3660254037844386`, 0.3660254037844386}, {-1., 0.}}, { {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[0.], ArrowBox[{{1, 2}, {1, 6}, {1, 10}, {1, 14}, {2, 3}, {2, 4}, {2, 5}, {6, 7}, {6, 8}, {6, 9}, {10, 11}, {10, 12}, { 10, 13}}, 0.03347773481857537]}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], DiskBox[1, 0.03347773481857537], DiskBox[2, 0.03347773481857537], DiskBox[3, 0.03347773481857537], DiskBox[4, 0.03347773481857537], DiskBox[5, 0.03347773481857537], DiskBox[6, 0.03347773481857537], DiskBox[7, 0.03347773481857537], DiskBox[8, 0.03347773481857537], DiskBox[9, 0.03347773481857537], DiskBox[10, 0.03347773481857537], DiskBox[11, 0.03347773481857537], DiskBox[12, 0.03347773481857537], DiskBox[13, 0.03347773481857537], DiskBox[14, 0.03347773481857537]}}]], MouseAppearanceTag["NetworkGraphics"]], AllowKernelInitialization->False]], DefaultBaseStyle->"NetworkGraphics", FormatType->TraditionalForm, FrameTicks->None]\)]$