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BUILT-IN MATHEMATICA SYMBOL

SimpleGraphQ

SimpleGraphQ[g]
yields True if the graph g is a simple graph and False otherwise.

A graph is simple if it has no self-loops or multiple edges between the same vertices.

Test whether a graph is simple:

Non-simple graphs:

Test whether a graph is simple:

Out[1]=

Out[2]=

Out[3]=

Non-simple graphs:

Out[1]=

Test undirected and directed graphs:

SimpleGraphQ gives False for expressions that are not simple graphs:

Test large graphs:

A graph with self-loops is not simple:

A simple graph can have a cycle:

A simple graph can be bipartite:

A PathGraph is always simple:

The adjacency matrix of a simple graph has zeros on the diagonal:

The incidence matrix of a simple graph has entries -1, 0, or 1:

All vertices of a simple graph have maximum degree less than the number of vertices:

A nontrivial simple graph must have at least one pair of vertices with the same degree:

A simple graph can have two edges between the same vertices but with opposite direction:

SimpleGraphQ gives False for non-explicit graphs: