triangles#

triangles(G, nodes=None)[source]#

Compute the number of triangles.

Finds the number of triangles that include a node as one vertex.

Parameters:

Ggraph: A networkx graph
nodesnode, iterable of nodes, or None (default=None): If a singleton node, return the number of triangles for that node. If an iterable, compute the number of triangles for each of those nodes. If None (the default) compute the number of triangles for all nodes in G.

Returns:

outdict or int: If nodes is a container of nodes, returns number of triangles keyed by node (dict). If nodes is a specific node, returns number of triangles for the node (int).

Notes

Self loops are ignored.

Examples

>>> G = nx.complete_graph(5)
>>> print(nx.triangles(G, 0))
6
>>> print(nx.triangles(G))
{0: 6, 1: 6, 2: 6, 3: 6, 4: 6}
>>> print(list(nx.triangles(G, [0, 1]).values()))
[6, 6]

The total number of unique triangles in G can be determined by summing the number of triangles for each node and dividing by 3 (because a given triangle gets counted three times, once for each of its nodes).

>>> sum(nx.triangles(G).values()) // 3
10