LoopFreeGraphQ

LoopFreeGraphQ[g]
yields True if the graph g has no self-loops, and False otherwise.

Test whether a graph has no self-loops:

LoopFreeGraphQ gives False for a graph with self-loops:

Test whether a graph has no self-loops:

Out[1]=

Out[2]=

Out[3]=

LoopFreeGraphQ gives False for a graph with self-loops:

Out[1]=

Test undirected and directed graphs:

LoopFreeGraphQ gives False for anything that is not a graph without self-loops:

Test large graphs:

A bipartite graph has no self-loops:

A TreeGraph has no self-loops:

A typical PathGraph has no self-loops:

The adjacency matrix of a graph without self-loops has a zero diagonal:

The incidence matrix of a graph without self-loops has no entries greater than 1:

LoopFreeGraphQ gives False for non-explicit graphs: