## Multi Graphs

General discussion about Mathematica features and functionality...
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### Multi Graphs

1. Can someone tell me why I am not getting a multi graph by typing the following command?

GraphPlot[{{0, 2}, {2, 0}}//MatrixForm]

2. For a given multi graph I know how to find its Adjacency Matrix but I am unable to draw a multi graph corresponding to a given matrix. Please help.

Keerti_Vardhan

Posts: 5
Joined: Thu Apr 22, 2010 1:37 pm
Organization: Panjab University
Department: Mathematics

### Re: Multi Graphs

The expression {{0, 2}, {2, 0}} is already a matrix, and MatrixForm doesn't help here.

The entries in a matrix that defines a graph are taken to be weights, not numbers of edges. I've used this function to draw multigraphs. It assumes that the matrix entries are nonnegative integers:

Code: Select all
`MultiEdgeList[g_] := Module[{edgelist = {}},  NestWhile[(edgelist = Join[edgelist, EdgeList[#]];      Map[Max[0, # - 1] &, #, {2}]) &, g, (Plus @@ Flatten[#] > 0) &];   Map[Rule @@ # &, edgelist]]`

This will then draw the graph I think you expect to see:

Code: Select all
`GraphPlot[MultiEdgeList[{{0, 2}, {2, 0}}], DirectedEdges -> True]`

Ken Levasseur
UMass Lowell

Ken_Levasseur

Posts: 1
Joined: Mon Feb 01, 2010 6:14 pm
Organization: UMass Lowell
Department: Mathematical Sciences

### Re: Multi Graphs

Dear Ken_Levasseur
Thanks for your reply. Later I found following command to plot multi graphs
GraphPlot[{{0,2},{2,0}},MultiedgeStyle -> True]

Kindly let me know the purpose of your first code i.e.
MultiEdgeList[g_] := Module[{edgelist = {}},NestWhile[(edgelist = Join[edgelist, EdgeList[#]];
Map[Max[0, # - 1] &, #, {2}]) &, g, (Plus @@ Flatten[#] > 0) &];
Map[Rule @@ # &, edgelist]].

I am unable to use this code on my computer.

Regards
Keerti Vardhan

Keerti_Vardhan

Posts: 5
Joined: Thu Apr 22, 2010 1:37 pm
Organization: Panjab University
Department: Mathematics