Прикладные области

Нахождение в графе компонент K-ядро

Система Mathematica 8 позволяет производить иерархическое разложение графа на

-ядра, используя команду KCoreComponents.

In[1]:=

g = \!\(\*

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, 21}, {

Null, {{1, 2}, {1, 3}, {1, 4}, {1, 15}, {2, 3}, {2, 4}, {3,

4}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {8,

9}, {8, 10}, {9, 10}, {10, 11}, {10, 12}, {10, 18}, {10,

19}, {11, 12}, {15, 16}, {16, 5}, {16, 17}}}, {

VertexSize -> {Large}, VertexCoordinates -> CompressedData["

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dYDQO+1h7oLKQ+kHaOJwcAC7v1jgNMxcCM3ocPYMCPA4GIPB5/0A3uZ4bQ==

"]}]], Typeset`boxes = GraphicsGroupBox[{{

Directive[

Hue[0.6, 0.2, 0.8],

EdgeForm[

Directive[

GrayLevel[0],

Opacity[0.7]]]],

TagBox[

DiskBox[{0., 0.}, 0.12393136749274763`], "DynamicName",

BoxID -> "VertexID$1"],

TagBox[

DiskBox[{0.8660254037844388, -0.4999999999999998},

0.12393136749274763`], "DynamicName",

BoxID -> "VertexID$2"],

TagBox[

DiskBox[{-0.8660254037844384, -0.5000000000000004},

0.12393136749274763`], "DynamicName",

BoxID -> "VertexID$3"],

TagBox[

DiskBox[{-2.4492935982947064`*^-16, 1.}, 0.12393136749274763`],

"DynamicName", BoxID -> "VertexID$4"],

TagBox[

DiskBox[{2., -1.}, 0.12393136749274763`], "DynamicName",

BoxID -> "VertexID$5"],

TagBox[

DiskBox[{2.866025403784439, -1.4999999999999998`},

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BoxID -> "VertexID$6"],

TagBox[

DiskBox[{1.1339745962155616`, -1.5000000000000004`},

0.12393136749274763`], "DynamicName",

BoxID -> "VertexID$7"],

TagBox[

DiskBox[{1.9999999999999998`, 0.}, 0.12393136749274763`],

"DynamicName", BoxID -> "VertexID$8"],

TagBox[

DiskBox[{1.5669872981077808`, 0.7499999999999998},

0.12393136749274763`], "DynamicName",

BoxID -> "VertexID$9"],

TagBox[

DiskBox[{1.9999999999999998`, 1.5}, 0.12393136749274763`],

"DynamicName", BoxID -> "VertexID$10"],

TagBox[

DiskBox[{3.066987298107781, 0.7499999999999998},

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BoxID -> "VertexID$11"],

TagBox[

DiskBox[{3.5, 1.5}, 0.12393136749274763`], "DynamicName",

BoxID -> "VertexID$12"],

TagBox[

DiskBox[{-0.5, 1.5}, 0.12393136749274763`], "DynamicName",

BoxID -> "VertexID$13"],

TagBox[

DiskBox[{3.7, 0.1}, 0.12393136749274763`], "DynamicName",

BoxID -> "VertexID$14"],

TagBox[

DiskBox[{-1., -1.5}, 0.12393136749274763`], "DynamicName",

BoxID -> "VertexID$15"],

TagBox[

DiskBox[{0.5, -1.}, 0.12393136749274763`], "DynamicName",

BoxID -> "VertexID$16"],

TagBox[

DiskBox[{0., -2.}, 0.12393136749274763`], "DynamicName",

BoxID -> "VertexID$17"],

TagBox[

DiskBox[{1., 2.}, 0.12393136749274763`], "DynamicName",

BoxID -> "VertexID$18"],

TagBox[

DiskBox[{2.5, 2.5}, 0.12393136749274763`], "DynamicName",

BoxID -> "VertexID$19"],

TagBox[

DiskBox[{0.1, 2.2}, 0.12393136749274763`], "DynamicName",

BoxID -> "VertexID$20"],

TagBox[

DiskBox[{3.6, -1.2}, 0.12393136749274763`], "DynamicName",

BoxID -> "VertexID$21"]}, {

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$3", Automatic, Center]}, {

DynamicLocation["VertexID$1", Automatic, Center],

DynamicLocation["VertexID$4", Automatic, Center]}, {

DynamicLocation["VertexID$1", Automatic, Center],

DynamicLocation["VertexID$15", Automatic, Center]}, {

DynamicLocation["VertexID$2", Automatic, Center],

DynamicLocation["VertexID$3", Automatic, Center]}, {

DynamicLocation["VertexID$2", Automatic, Center],

DynamicLocation["VertexID$4", Automatic, Center]}, {

DynamicLocation["VertexID$3", Automatic, Center],

DynamicLocation["VertexID$4", Automatic, Center]}, {

DynamicLocation["VertexID$5", Automatic, Center],

DynamicLocation["VertexID$6", Automatic, Center]}, {

DynamicLocation["VertexID$5", Automatic, Center],

DynamicLocation["VertexID$7", Automatic, Center]}, {

DynamicLocation["VertexID$5", Automatic, Center],

DynamicLocation["VertexID$8", Automatic, Center]}, {

DynamicLocation["VertexID$5", Automatic, Center],

DynamicLocation["VertexID$16", Automatic, Center]}, {

DynamicLocation["VertexID$6", Automatic, Center],

DynamicLocation["VertexID$7", Automatic, Center]}, {

DynamicLocation["VertexID$6", Automatic, Center],

DynamicLocation["VertexID$8", Automatic, Center]}, {

DynamicLocation["VertexID$7", Automatic, Center],

DynamicLocation["VertexID$8", Automatic, Center]}, {

DynamicLocation["VertexID$8", Automatic, Center],

DynamicLocation["VertexID$9", Automatic, Center]}, {

DynamicLocation["VertexID$8", Automatic, Center],

DynamicLocation["VertexID$10", Automatic, Center]}, {

DynamicLocation["VertexID$9", Automatic, Center],

DynamicLocation["VertexID$10", Automatic, Center]}, {

DynamicLocation["VertexID$10", Automatic, Center],

DynamicLocation["VertexID$11", Automatic, Center]}, {

DynamicLocation["VertexID$10", Automatic, Center],

DynamicLocation["VertexID$12", Automatic, Center]}, {

DynamicLocation["VertexID$10", Automatic, Center],

DynamicLocation["VertexID$18", Automatic, Center]}, {

DynamicLocation["VertexID$10", Automatic, Center],

DynamicLocation["VertexID$19", Automatic, Center]}, {

DynamicLocation["VertexID$11", Automatic, Center],

DynamicLocation["VertexID$12", Automatic, Center]}, {

DynamicLocation["VertexID$15", Automatic, Center],

DynamicLocation["VertexID$16", Automatic, Center]}, {

DynamicLocation["VertexID$16", Automatic, Center],

DynamicLocation["VertexID$17", Automatic, Center]}}]}}]},

DynamicBox[GraphComputation`NetworkGraphicsBox[

1, Typeset`graph, Typeset`boxes], {

CachedValue :> Typeset`boxes, SingleEvaluation -> True,

SynchronousUpdating -> False, TrackedSymbols :> {}},

ImageSizeCache->{{3.920000000000001, 242.08}, {-116.27679999999998`,

112.33726016095989`}}]]],

DefaultBaseStyle->{

"NetworkGraphics",

FrontEnd`GraphicsHighlightColor -> Hue[0.8, 1., 0.6]},

FrameTicks->None,

ImageSize->{247., Automatic}]\);

In[2]:=

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In[4]:=

Out[4]=