BUILT-IN MATHEMATICA SYMBOL

EdgeCount

EdgeCount[g]
gives a count of the number of edges in the graph g.

EdgeCount

gives a count of the number of edges that match the pattern patt.

MORE INFORMATION

Multiple edges between nodes are counted as separate.

EXAMPLES

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Basic Examples (2)

Count the number of edges:

Count the number of edges that match a pattern:

The number of edges incident to 1:

Count the number of edges:

In[1]:=

Out[1]=

In[2]:=

Out[2]=

Count the number of edges that match a pattern:

In[1]:=

Out[1]=

The number of edges incident to 1:

In[2]:=

Out[2]=

Scope (3)

EdgeCount works with undirected graphs:

Directed graphs:

Works with large graphs:

Generalizations & Extensions (1)

Count the number of edges on symbolic graph constructors:

Applications (2)

The minimum number of edges in a connected graph with

vertices is

:

A path graph with

vertices has exactly

edges:

The number of edges for Bernoulli graphs with probability

on

vertices has mean

:

The standard deviation is

:

The full distribution:

Properties & Relations (7)

The number of edges of CompleteGraph[n]:

EdgeCount can be found using EdgeList:

The number of edges for a directed graph can be found from matrix representations:

Totaling the adjacency matrix:

The number of columns of the incidence matrix:

The number of edges for an undirected graph can be found from matrix representations:

The total of the upper (or lower) triangular part of the adjacency matrix:

The number of columns of the incidence matrix:

Totaling the diagonal elements of the Kirchhoff matrix, divided by 2:

The number of edges of the graph is equal to the number of vertices of its line graph:

The sum of the degrees of all vertices of a graph is twice the number of edges:

The underlying undirected graph of a graph g has the same number of edges as g: