triadic_census

triadic_census(G, nodelist=None)

Determines the triadic census of a directed graph.

The triadic census is a count of how many of the 16 possible types of triads are present in a directed graph. If a list of nodes is passed, then only those triads are taken into account which have elements of nodelist in them.

Parameters:

Gdigraph

A NetworkX DiGraph

nodelistlist

List of nodes for which you want to calculate triadic census

Returns:

censusdict

Dictionary with triad type as keys and number of occurrences as values.

Raises:

ValueError

If nodelist contains duplicate nodes or nodes not in G. If you want to ignore this you can preprocess with set(nodelist) & G.nodes

See also

triad_graph

Notes

This algorithm has complexity \(O(m)\) where \(m\) is the number of edges in the graph.

For undirected graphs, the triadic census can be computed by first converting the graph into a directed graph using the G.to_directed() method. After this conversion, only the triad types 003, 102, 201 and 300 will be present in the undirected scenario.

References

[1]

Vladimir Batagelj and Andrej Mrvar, A subquadratic triad census algorithm for large sparse networks with small maximum degree, University of Ljubljana, http://vlado.fmf.uni-lj.si/pub/networks/doc/triads/triads.pdf

Examples

>>> G = nx.DiGraph([(1, 2), (2, 3), (3, 1), (3, 4), (4, 1), (4, 2)])
>>> triadic_census = nx.triadic_census(G)
>>> for key, value in triadic_census.items():
...     print(f"{key}: {value}")
003: 0
012: 0
102: 0
021D: 0
021U: 0
021C: 0
111D: 0
111U: 0
030T: 2
030C: 2
201: 0
120D: 0
120U: 0
120C: 0
210: 0
300: 0