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# Stochastic block model

Hi all,

I would like to draw a random graph by Sage. The general stochastic model is the following: The graph contains $n$ vertices and the n vertices are divided into $r$ communities $C_1\cdots,C_r$. For two vertices within the same community, there is a probability $P_r$ that they are connected directly by an edge. How do I plot such a graph in Sage? References appreciated.

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## Comments

Maybe use

sage: SetPartitions(5).random_element()
{{1, 5}, {2, 4}, {3}}

( 2017-09-22 10:50:00 +0100 )edit

Are the sizes of the communities given as part of the input? Maybe this is what the comment above is trying to address.

Is the probability of edges between vertices in different communities equal to 0?

( 2017-09-22 12:06:05 +0100 )edit

## 1 Answer

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Assuming the input consists of n, r, and the probabilities for edges within a community; and assuming that the probability of edges between vertices in different communities is 0, then here is a possible way to generate such a graph.

community_sizes = Partitions(n,length=r).random_element()
H = Graph()
for comm_size,Pr in zip(community_sizes,probs):
H=H.disjoint_union(graphs.RandomGNP(comm_size,Pr),labels='integers')


This is assuming that n, r and probs (assumed to be a list of length r containing $P_1,P_2,\ldots,P_r$) are given as part of the input. To see the resulting graph you can use H.show().

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Asked: 2017-09-21 20:19:26 +0100

Seen: 380 times

Last updated: Sep 22 '17