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
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Additional backends implement this function

cugraph : GPU-accelerated backend.

graphblas : OpenMP-enabled sparse linear algebra backend.

parallelA networkx backend that uses joblib to run graph algorithms in parallel. Find the nx-parallel’s configuration guide here

The nodes are chunked into node_chunks and for all node_chunks the number of triangles that include a node as one vertex is computed in parallel over n_jobs number of CPU cores.

Additional parameters:

get_chunksstr, function (default = “chunks”): A function that takes in a list of all the nodes (or nbunch) as input and returns an iterable node_chunks. The default chunking is done by slicing the nodes into n_jobs number of chunks.

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