How to create a connected graph in networkx

Question

I want to create a connected graph in IPython notebook through NetworkX . Previously, I use

erdos_renyi_graph

to generate a random graph, but I never get a connected graph, I want to use this graph to prove that my graph is a small world network. But the unconnected graph's average shortest path cannot be calculated. So please tell me how to generate a connected graph through NetworkX .

Answer 1

As you didn't mention the exact parameters of your graph I want to suggest playing with the probability of creating edges. The following networkx function allows you to provide a probability (p) for an edge to exist in the graph.

erdos_renyi_graph(n, p, seed=None, directed=False)

As an example:

G = nx.erdos_renyi_graph(500, 0.5, seed=123, directed=False)

provides you a fully connected graph.

Answer 2

There are a lot of graph generators for NetworkX defined, you can use not only the erdos_renyi_graph (which can be adjusted to nearly connected by second parameter):

Social Networks graphs for you:

• karate_club_graph() - Return Zachary's Karate club graph .
• davis_southern_women_graph() - Return Davis Southern women social network .
• florentine_families_graph() - Return Florentine families graph .

Community graphs :

• caveman_graph(l, k) - Returns a caveman graph of l cliques of size k .
• connected_caveman_graph(l, k) - Returns a connected caveman graph of n cliques of size k .
• relaxed_caveman_graph(l, k, p[, seed, directed]) - Return a relaxed caveman graph .
• random_partition_graph(sizes, p_in, p_out[, ...]) - Return the random partition graph with a partition of sizes.
• planted_partition_graph(l, k, p_in, p_out[, ...]) - Return the planted l -partition graph .
• gaussian_random_partition_graph(n, s, v, ...) - Generate a Gaussian random partition graph .
• ring_of_cliques

and so on.