non_randomness(G, k=None)[source]

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.

  • G (NetworkX graph) – Graph must be binary, symmetric, connected, and without self-loops.

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


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

Return type

(float, float) tuple


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


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



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