How to create random graph?

Hi ,

I want to check whether the network that I have obtained is a small world network or not. For that I have to find out the clustering coefficient and shortest path length of a random network with the same number of nodes and links in my network. Is it possible to find out?

Answer 1

[Christine Tobler]

You can use

s = randi(n, e, 1);
t = randi(n, e, 1);
G = graph(s, t, [], n);

which will give you a graph with n nodes and e edges. Note that G may have multiple edges connecting the same two nodes, and may also have self-loops (edges connecting a node to itself). If you don't want repeating edges, use the following instead:

G = graph(true(n)); % Self-loops are possible
%G = graph(true(n), 'omitselfloops'); % Alternative without self-loops
p = randperm(numedges(G), e);
G = graph(G.Edges(p, :));

[Rayan Glus]

Thanks Christine!

Is what you wrote the same as Erdos - Renyi random graph model? I'm sorry for the stupid question.

[Christine Tobler]

Hi Rayan, great question!

The second code I included matches the G(n, M) model of Erdos-Renyi (usually would be done omitting self-loops). The first code doesn't match any of the Erdos-Renyi models, since it can generate multiple edges between the same two nodes.

You can generate the G(n, p) model of Erdos-Renyi by the following code (notice I renamed variable p above, since this is now needed for the probability of each edge being in the graph).

G = graph(true(n), 'omitselfloops');
edgesToKeep = rand(numedges(G), 1) < p;
G = graph(G.Edges(edgesToKeep, :));

Note for both variants, this could probably be computed in a faster way by avoiding the creation of G and instead coming up with some code that does the mapping from an edge ID in the complete graph with n nodes into the source and target node of that edge. But this is much more compact and simple code.

[Rayan Glus]

Thank you so much for the nice clarification, Christine.

Your code was able to generate a graph of 6000 nodes with p=0.6, and then plot it in just couple of seconds.

[Norbert Cyran]

Why are you generating true matrix for nodes and random values for edges??

[Christine Tobler]

Hi Norbert,

The true(n) matrix is an adjacency matrix that contains all possible edges in the graph (omitting self-loops or not depending if that option is used or not). Then, I'm choosing a random subset of those edges using the randperm function.

Answer 2

[Deepthi B]

Thank You