is_simple_path

is_simple_path(G, nodes)

Returns True if and only if nodes form a simple path in G.

A simple path in a graph is a nonempty sequence of nodes in which no node appears more than once in the sequence, and each adjacent pair of nodes in the sequence is adjacent in the graph.

Parameters

Ggraph

A NetworkX graph.

nodeslist

A list of one or more nodes in the graph G.

Returns

bool

Whether the given list of nodes represents a simple path in G.

Notes

An empty list of nodes is not a path but a list of one node is a path. Here’s an explanation why.

This function operates on node paths. One could also consider edge paths. There is a bijection between node paths and edge paths.

The length of a path is the number of edges in the path, so a list of nodes of length n corresponds to a path of length n - 1. Thus the smallest edge path would be a list of zero edges, the empty path. This corresponds to a list of one node.

To convert between a node path and an edge path, you can use code like the following:

>>> from networkx.utils import pairwise
>>> nodes = [0, 1, 2, 3]
>>> edges = list(pairwise(nodes))
>>> edges
[(0, 1), (1, 2), (2, 3)]
>>> nodes = [edges[0][0]] + [v for u, v in edges]
>>> nodes
[0, 1, 2, 3]

Examples

>>> G = nx.cycle_graph(4)
>>> nx.is_simple_path(G, [2, 3, 0])
True
>>> nx.is_simple_path(G, [0, 2])
False