This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)


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:
Click for copyable input
Click for copyable input
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