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 C1⋯,Cr. For two vertices within the same community, there is a probability Pr that they are connected directly by an edge. How do I plot such a graph in Sage? References appreciated.
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 P1,P2,…,Pr) are given as part of the input. To see the resulting graph you can use H.show().
Asked: 7 years ago
Seen: 481 times
Last updated: Sep 22 '17
Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.
Maybe use
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?