gg=GridGraph[{10,10}]
In[]:=
Out[]=
GraphCenter[gg]
In[]:=
{45,46,55,56}
Out[]=
NeighborhoodGraph[gg,46,4]
In[]:=
Out[]=
GraphAntipodes[%]
In[]:=
{6,77}
Out[]=
HighlightGraph[%7,FindShortestPath[%7,6,77]]
In[]:=
Out[]=
GraphPeriphery

In[]:=
{6,15,17,24,28,33,39,42,50,53,59,64,68,75,77,86}
Out[]=
AllGeodesics[g_]:=Module[{m=GraphDistanceMatrix[g],v=VertexList[g]},Map[v[[#]]&,Position[m,Max[m]],{2}]]
In[]:=
AllGeodesics

In[]:=
Out[]=
HighlightGraph
,FindShortestPath
,#1,#2&@@@Take[%15,6]
In[]:=
Out[]=
FindShortestPath[%7,6,77]
In[]:=
{6,16,17,27,37,47,57,67,77}
Out[]=
GraphDistance[%7,86,%]
In[]:=
GraphDistance
:The argument 86 in
GraphDistance[Graph[<41>, <64>], 86, {6, 16, 17, 27, 37, 47, 57, 67, 77}]
is not a valid vertex.
Out[]=
Subgraph
,{6,16,17,27,37,47,57,67,77}
In[]:=
Out[]=
GraphDistance
,86,

In[]:=
GraphDistance
:The argument 86 in
GraphDistance[Graph[<41>, <64>], 86, Graph[<9>, <8>]]
is not a valid vertex.
Out[]=
GraphLineDistance[g_,start_,line_]:=Min[GraphDistance[g,start,#]&/@line]
In[]:=
GraphLineDistance
,86,{6,16,17,27,37,47,57,67,77}
In[]:=
2
Out[]=
SortByAllGeodesics
,TotalGraphLineDistance
,#,{6,16,17,27,37,47,57,67,77}&/@#&
In[]:=
Out[]=