BUILT-IN MATHEMATICA SYMBOL

PathGraphQ

PathGraphQ[g]
yields True if the graph g is a path and False otherwise.

MORE INFORMATION

An undirected path graph is a connected graph where each vertex has at most degree two.

A directed path graph is a connected graph where each vertex has at most in-degree one and at most out-degree one.

EXAMPLES

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Basic Examples (2)

Test whether a graph is a path:

The vertex degree is at most 2:

A complete graph is not a path:

The vertex degree is greater than 2:

Test whether a graph is a path:

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The vertex degree is at most 2:

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A complete graph is not a path:

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The vertex degree is greater than 2:

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Scope (3)

Test undirected and directed graphs:

PathGraphQ gives False for anything that is not a path graph:

Test large graphs:

Properties & Relations (8)

A path graph is loop-free if it has more than one vertex:

A one-vertex path graph can have a loop:

A path graph does not necessarily have edges:

Or vertices:

A path graph that starts and ends in the same vertex is a cycle graph:

A path graph with no repeated vertices is a tree:

An acyclic path graph is simple:

And also bipartite:

GridGraph

are all path graphs:

A path graph is connected and each vertex has at most degree 2:

The line graph of a path

is isomorphic to

:

Possible Issues (1)

PathGraphQ gives False for non-explicit graphs: