Re: number of Trangles in a graph-network

• To: mathgroup at smc.vnet.net
• Subject: [mg99373] Re: number of Trangles in a graph-network
• From: Peter Pein <petsie at dordos.net>
• Date: Mon, 4 May 2009 06:00:18 -0400 (EDT)
• References: <gtefaf\$197\$1@smc.vnet.net>

```Luca Cinacchio schrieb:
> Greetings,
>
> having a graph (network, i.e. one created with RandomGraph) wich can have
> not connected nodes, I would like to count the total number of triangles
> inside the graph.
> I gave a look to Combinatorica and its related book by Pemmaraju Skiena,
> but I did'nt find any solution (maybe I am wrong). Do you know if there is
> a easy way to answer this problem with Mathematica and/or Combinatorica?
>

The following does not check for triples of points being colinear, but it
seems to be a possible starting point:

In[1]:= <<Combinatorica`
In[2]:= List@@(rg=RandomGraph[7,2/3])
Out[2]=
{{{{1,2}},{{1,3}},{{2,3}},{{1,4}},{{2,4}},{{3,4}},{{2,5}},{{4,5}},{{1,6}},{{2,6}},{{3,6}},{{1,7}},{{3,7}},{{4,7}},{{6,7}}},
{{{0.62349,0.781831}},{{-0.222521,0.974928}},{{-0.900969,0.433884}},{{-0.900969,-0.433884}},{{-0.222521,-0.974928}},{{0.62349,-0.781831}},{{1.,0}}}}
In[3]:= GraphPlot@rg
..graphics..
In[4]:=
Total[ReplaceList[rg[[1]],{___,{{a_,b_}},___,{{a_,c_}},___,{{b_,c_}},___}:>1]]
Out[4]= 13

Peter

```

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