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.
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.
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.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_cliquesand so on.
