Application Areas

Center, Periphery, and Distance Functions

Mathematica 8 provides functions related to minimum and maximum vertex eccentricities.

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}, {{{1, 3}, {1, 8}, {2, 4}, {2, 7}, {3, 10}, {4, 6}, {5,

7}, {6, 13}, {7, 14}, {8, 9}, {10, 11}, {13, 14}, {14, 8}, {

6, 1}, {9, 2}, {5, 3}, {11, 4}, {12, 5}, {10, 9}, {12,

11}, {13, 12}}, Null}, {

EdgeShapeFunction -> {"Arrow"}, EdgeStyle -> {

Directive[

Thickness[Large],

Arrowheads[Medium]]}, VertexSize -> {Medium},

VertexCoordinates -> {{0.7818314824680297,

0.6234898018587336}, {

0.9749279121818236, -0.22252093395631434`}, {

0.43388373911755823`, -0.900968867902419}, \

{-0.433883739117558, -0.9009688679024191}, {-0.9749279121818235, \

-0.2225209339563146}, {-0.7818314824680299,

0.6234898018587334}, {-2.4492935982947064`*^-16, 1.}, {

1.5636629649360594`, 1.2469796037174672`}, {

1.9498558243636472`, -0.4450418679126287}, {

0.8677674782351165, -1.801937735804838}, \

{-0.867767478235116, -1.8019377358048383`}, {-1.949855824363647, \

-0.4450418679126292}, {-1.5636629649360598`,

1.2469796037174667`}, {-4.898587196589413*^-16, 2.}}}]],

Typeset`boxes = GraphicsGroupBox[{{

Directive[

Hue[0.6, 0.2, 0.8],

EdgeForm[

Directive[

GrayLevel[0],

Opacity[0.7]]]],

TagBox[

DiskBox[{0.7818314824680297, 0.6234898018587336},

0.08677674782351162], "DynamicName",

BoxID -> "VertexID$1"],

TagBox[

DiskBox[{0.9749279121818236, -0.22252093395631434`},

0.08677674782351162], "DynamicName",

BoxID -> "VertexID$2"],

TagBox[

DiskBox[{0.43388373911755823`, -0.900968867902419},

0.08677674782351162], "DynamicName",

BoxID -> "VertexID$3"],

TagBox[

DiskBox[{-0.433883739117558, -0.9009688679024191},

0.08677674782351162], "DynamicName",

BoxID -> "VertexID$4"],

TagBox[

DiskBox[{-0.9749279121818235, -0.2225209339563146},

0.08677674782351162], "DynamicName",

BoxID -> "VertexID$5"],

TagBox[

DiskBox[{-0.7818314824680299, 0.6234898018587334},

0.08677674782351162], "DynamicName",

BoxID -> "VertexID$6"],

TagBox[

DiskBox[{-2.4492935982947064`*^-16, 1.}, 0.08677674782351162],

"DynamicName", BoxID -> "VertexID$7"],

TagBox[

DiskBox[{1.5636629649360594`, 1.2469796037174672`},

0.08677674782351162], "DynamicName",

BoxID -> "VertexID$8"],

TagBox[

DiskBox[{1.9498558243636472`, -0.4450418679126287},

0.08677674782351162], "DynamicName",

BoxID -> "VertexID$9"],

TagBox[

DiskBox[{0.8677674782351165, -1.801937735804838},

0.08677674782351162], "DynamicName",

BoxID -> "VertexID$10"],

TagBox[

DiskBox[{-0.867767478235116, -1.8019377358048383`},

0.08677674782351162], "DynamicName",

BoxID -> "VertexID$11"],

TagBox[

DiskBox[{-1.949855824363647, -0.4450418679126292},

0.08677674782351162], "DynamicName",

BoxID -> "VertexID$12"],

TagBox[

DiskBox[{-1.5636629649360598`, 1.2469796037174667`},

0.08677674782351162], "DynamicName",

BoxID -> "VertexID$13"],

TagBox[

DiskBox[{-4.898587196589413*^-16, 2.}, 0.08677674782351162],

"DynamicName", BoxID -> "VertexID$14"]}, {

Directive[

Opacity[0.7],

Hue[0.6, 0.7, 0.5]],

Directive[

Thickness[Large],

Arrowheads[Medium]],

StyleBox[{

ArrowBox[{

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

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

Directive[

Thickness[Large],

Arrowheads[Medium]], StripOnInput -> False],

StyleBox[{

ArrowBox[{

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

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

Directive[

Thickness[Large],

Arrowheads[Medium]], StripOnInput -> False],

StyleBox[{

ArrowBox[{

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

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

Directive[

Thickness[Large],

Arrowheads[Medium]], StripOnInput -> False],

StyleBox[{

ArrowBox[{

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

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

Directive[

Thickness[Large],

Arrowheads[Medium]], StripOnInput -> False],

StyleBox[{

ArrowBox[{

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

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

Directive[

Thickness[Large],

Arrowheads[Medium]], StripOnInput -> False],

StyleBox[{

ArrowBox[{

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

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

Directive[

Thickness[Large],

Arrowheads[Medium]], StripOnInput -> False],

StyleBox[{

ArrowBox[{

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

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

Directive[

Thickness[Large],

Arrowheads[Medium]], StripOnInput -> False],

StyleBox[{

ArrowBox[{

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

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

Directive[

Thickness[Large],

Arrowheads[Medium]], StripOnInput -> False],

StyleBox[{

ArrowBox[{

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

DynamicLocation["VertexID$13", Automatic, Center]}]},

Directive[

Thickness[Large],

Arrowheads[Medium]], StripOnInput -> False],

StyleBox[{

ArrowBox[{

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

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

Directive[

Thickness[Large],

Arrowheads[Medium]], StripOnInput -> False],

StyleBox[{

ArrowBox[{

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

DynamicLocation["VertexID$14", Automatic, Center]}]},

Directive[

Thickness[Large],

Arrowheads[Medium]], StripOnInput -> False],

StyleBox[{

ArrowBox[{

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

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

Directive[

Thickness[Large],

Arrowheads[Medium]], StripOnInput -> False],

StyleBox[{

ArrowBox[{

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

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

Directive[

Thickness[Large],

Arrowheads[Medium]], StripOnInput -> False],

StyleBox[{

ArrowBox[{

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

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

Directive[

Thickness[Large],

Arrowheads[Medium]], StripOnInput -> False],

StyleBox[{

ArrowBox[{

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

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

Directive[

Thickness[Large],

Arrowheads[Medium]], StripOnInput -> False],

StyleBox[{

ArrowBox[{

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

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

Directive[

Thickness[Large],

Arrowheads[Medium]], StripOnInput -> False],

StyleBox[{

ArrowBox[{

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

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

Directive[

Thickness[Large],

Arrowheads[Medium]], StripOnInput -> False],

StyleBox[{

ArrowBox[{

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

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

Directive[

Thickness[Large],

Arrowheads[Medium]], StripOnInput -> False],

StyleBox[{

ArrowBox[{

DynamicLocation["VertexID$13", Automatic, Center],

DynamicLocation["VertexID$14", Automatic, Center]}]},

Directive[

Thickness[Large],

Arrowheads[Medium]], StripOnInput -> False],

StyleBox[{

ArrowBox[{

DynamicLocation["VertexID$13", Automatic, Center],

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

Directive[

Thickness[Large],

Arrowheads[Medium]], StripOnInput -> False],

StyleBox[{

ArrowBox[{

DynamicLocation["VertexID$14", Automatic, Center],

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

Directive[

Thickness[Large],

Arrowheads[Medium]], StripOnInput -> False]}}]},

DynamicBox[GraphComputation`NetworkGraphicsBox[

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

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

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

ImageSizeCache->{{2.140000000000006, 154.86}, {-76.98560000000003,

72.11654463499247}}]]],

DefaultBaseStyle->{

"NetworkGraphics",

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

FrameTicks->None,

ImageSize->{158., Automatic}]\);

In[2]:=

In[3]:=

Out[3]=