# SimpleGraph

SimpleGraph[g]

gives the underlying simple graph from the graph g.

SimpleGraph[{vw,}]

uses rules vw to specify the graph g.

# Details and Options • 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.
• SimpleGraph works with undirected graphs, directed graphs, multigraphs, and mixed graphs.

# Examples

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## Basic Examples(1)

Remove self-loops from a graph:

## Scope(6)

SimpleGraph works with undirected graphs:

Directed graphs:

Multigraph:

Mixed graph:

Use rules to specify the graph:

SimpleGraph works with large graphs:

## Properties & Relations(7)

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: