Random graphs with fixed numbers of neighbours

November 24, 2010

(This article was first published on Xi'an's Og » R, and kindly contributed to R-bloggers)

In connection with Le Monde puzzle #46, I eventually managed to write an R program that generates graphs with a given number n of nodes and a given number k of edges leaving each of those nodes. (My early attempt was simply too myopic to achieve any level of success when n was larger than 10!) Here is the core of the R code:

A=42 #number of nodes
L=13 #number of edges

if ((A*L)%%2==1){
 print("impossible graph")
 diag(con)=A      #eliminate self-connection

 while (min(suma)ApL-1)) vali=NULL

and it uses a sort of annealed backward step to avoid simulating a complete new collection of neighbours when reaching culs-de-sac….

#removes a random number of links among the nodes with L links

while (max(apply(con,1,sum))==ApL){

 if (sum(apply(con,1,sum)==ApL)==1){

There is nothing fancy or optimised about this code so I figure there are much better versions to be found elsewhere…

Ps-As noticed before, sample does not work on a set of length one, which is a bug in my opinion…. Instead, sample(4.5,1) returns a random permutation of (1,2,3,4).

> sample(4.5)
[1] 4 3 1 2

Filed under: R, Statistics Tagged: edges, graphs, Le Monde, nodes, simulation

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