# is_simple_path#

is_simple_path(G, nodes)[source]#

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] + [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
```