non_randomness#
- non_randomness(G, k=None, weight='weight')[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.
- 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')