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? > Thanks in advance. > 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