gives the underlying simple graph from the graph g.
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.
Examplesopen allclose all
SimpleGraph works with undirected graphs:
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:
Wolfram Research (2010), SimpleGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/SimpleGraph.html (updated 2015).
Wolfram Language. 2010. "SimpleGraph." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/SimpleGraph.html.
Wolfram Language. (2010). SimpleGraph. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SimpleGraph.html