all_triangles#

all_triangles(G, nbunch=None)[source]#

Yields all unique triangles in an undirected graph.

A triangle is a set of three distinct nodes where each node is connected to the other two.

Parameters:

GNetworkX graph: An undirected graph.
nbunchnode, iterable of nodes, or None (default=None): If a node or iterable of nodes, only triangles involving at least one node in nbunch are yielded. If None, yields all unique triangles in the graph.

Yields:

tuple: A tuple of three nodes forming a triangle (u, v, w).

See also

all_triads(): related function for directed graphs

Notes

This algorithm ensures each triangle is yielded once using an internal node ordering. In multigraphs, triangles are identified by their unique set of nodes, ignoring multiple edges between the same nodes. Self-loops are ignored. Runs in O(m * d) time in the worst case, where m the number of edges and d the maximum degree.

Examples

>>> G = nx.complete_graph(4)
>>> sorted([sorted(t) for t in all_triangles(G)])
[[0, 1, 2], [0, 1, 3], [0, 2, 3], [1, 2, 3]]