This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
 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.
Remove self-loops from a graph:
Remove self-loops from a graph:
 Out[1]=
 Out[2]=
 Scope   (3)
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:
New in 8