random_clustered_graph

random_clustered_graph(joint_degree_sequence, create_using=None, seed=None)

Generate a random graph with the given joint degree and triangle degree sequence.

This uses a configuration model-like approach to generate a random pseudograph (graph with parallel edges and self loops) by randomly assigning edges to match the given indepdenent edge and triangle degree sequence.

Parameters :

joint_degree_sequence : list of integer pairs

Each list entry corresponds to the independent edge degree and triangle degree of a node.

create_using : graph, optional (default MultiGraph)

Return graph of this type. The instance will be cleared.

seed : hashable object, optional

The seed for the random number generator.

Returns :

G : MultiGraph

A graph with the specified degree sequence. Nodes are labeled starting at 0 with an index corresponding to the position in deg_sequence.

Raises :

NetworkXError :

If the independent edge degree sequence sum is not even or the triangle degree sequence sum is not divisible by 3.

Notes

As described by Miller [R208] (see also Newman [R209] for an equivalent description).

A non-graphical degree sequence (not realizable by some simple graph) is allowed since this function returns graphs with self loops and parallel edges. An exception is raised if the independent degree sequence does not have an even sum or the triangle degree sequence sum is not divisible by 3.

This configuration model-like construction process can lead to duplicate edges and loops. You can remove the self-loops and parallel edges (see below) which will likely result in a graph that doesn’t have the exact degree sequence specified. This “finite-size effect” decreases as the size of the graph increases.

References

[R208]

(1, 2) J. C. Miller “Percolation and Epidemics on Random Clustered Graphs.” Physical Review E, Rapid Communication (to appear).

[R209]

(1, 2) M.E.J. Newman, “Random clustered networks”. Physical Review Letters (to appear).

Examples

>>> deg_tri=[[1,0],[1,0],[1,0],[2,0],[1,0],[2,1],[0,1],[0,1]]
>>> G = nx.random_clustered_graph(deg_tri)

To remove parallel edges:

>>> G=nx.Graph(G)

To remove self loops:

>>> G.remove_edges_from(G.selfloop_edges())