stochastic_block_model#

stochastic_block_model(sizes, p, nodelist=None, seed=None, directed=False, selfloops=False, sparse=True)[source]#

Returns a stochastic block model graph.

This model partitions the nodes in blocks of arbitrary sizes, and places edges between pairs of nodes independently, with a probability that depends on the blocks.

Parameters:

sizeslist of ints: Sizes of blocks
plist of list of floats: Element (r,s) gives the density of edges going from the nodes of group r to nodes of group s. p must match the number of groups (len(sizes) == len(p)), and it must be symmetric if the graph is undirected.
nodelistlist, optional: The block tags are assigned according to the node identifiers in nodelist. If nodelist is None, then the ordering is the range [0,sum(sizes)-1].
seedinteger, random_state, or None (default): Indicator of random number generation state. See Randomness.
directedboolean optional, default=False: Whether to create a directed graph or not.
selfloopsboolean optional, default=False: Whether to include self-loops or not.
sparse: boolean optional, default=True: Use the sparse heuristic to speed up the generator.

Returns:

gNetworkX Graph or DiGraph: Stochastic block model graph of size sum(sizes)

Raises:

NetworkXError: If probabilities are not in [0,1]. If the probability matrix is not square (directed case). If the probability matrix is not symmetric (undirected case). If the sizes list does not match nodelist or the probability matrix. If nodelist contains duplicate.

See also

random_partition_graph
planted_partition_graph
gaussian_random_partition_graph
gnp_random_graph

References

[1]

Holland, P. W., Laskey, K. B., & Leinhardt, S., “Stochastic blockmodels: First steps”, Social networks, 5(2), 109-137, 1983.

Examples

>>> sizes = [75, 75, 300]
>>> probs = [[0.25, 0.05, 0.02], [0.05, 0.35, 0.07], [0.02, 0.07, 0.40]]
>>> g = nx.stochastic_block_model(sizes, probs, seed=0)
>>> len(g)
450
>>> H = nx.quotient_graph(g, g.graph["partition"], relabel=True)
>>> for v in H.nodes(data=True):
...     print(round(v[1]["density"], 3))
0.245
0.348
0.405
>>> for v in H.edges(data=True):
...     print(round(1.0 * v[2]["weight"] / (sizes[v[0]] * sizes[v[1]]), 3))
0.051
0.022
0.07