THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.

DOCUMENTATION CENTER SEARCH

BUILT-IN MATHEMATICA SYMBOL

SimpleGraph

SimpleGraph[g]
gives the underlying simple graph from the graph g.

SimpleGraph[g] removes all self-loops and multiple edges between the same vertices.

SimpleGraph preserves directed edges as directed. UndirectedGraph can be used to compute the underlying undirected graph.

Remove self-loops from a graph:

Out[1]=

Out[2]=

SimpleGraph works with undirected graphs with self-loops:

Directed graphs with self-loops:

SimpleGraph works with large graphs:

A graph with self-loops is not simple:

A PathGraph is always simple:

A TreeGraph without multiple edges is simple:

The adjacency matrix of a simple graph has entries not greater than 1:

Diagonal elements are all zeros:

The incidence matrix of a simple graph has entries -1, 0, or 1 and no repeated column:

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

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