non_randomness

non_randomness(G, k=None, weight='weight')

Compute the non-randomness of graph G.

The first returned value nr is the sum of non-randomness values of all edges within the graph (where the non-randomness of an edge tends to be small when the two nodes linked by that edge are from two different communities).

The second computed value nr_rd is a relative measure that indicates to what extent graph G is different from random graphs in terms of probability. When it is close to 0, the graph tends to be more likely generated by an Erdos Renyi model.

Parameters:

GNetworkX graph

Graph must be symmetric, connected, and without self-loops.

kint

The number of communities in G. If k is not set, the function will use a default community detection algorithm to set it.

weightstring or None, optional (default=None)

The name of an edge attribute that holds the numerical value used as a weight. If None, then each edge has weight 1, i.e., the graph is binary.

Returns:

non-randomness(float, float) tuple

Non-randomness, Relative non-randomness w.r.t. Erdos Renyi random graphs.

Raises:

NetworkXException

if the input graph is not connected.

NetworkXError

if the input graph contains self-loops.

Notes

This computes Eq. (4.4) and (4.5) in Ref. [1].

If a weight field is passed, this algorithm will use the eigenvalues of the weighted adjacency matrix to compute Eq. (4.4) and (4.5).

References

[1]

Xiaowei Ying and Xintao Wu, On Randomness Measures for Social Networks, SIAM International Conference on Data Mining. 2009

Examples

>>> G = nx.karate_club_graph()
>>> nr, nr_rd = nx.non_randomness(G, 2)
>>> nr, nr_rd = nx.non_randomness(G, 2, 'weight')