This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# VertexOutDegree

 VertexOutDegree[g] gives the list of vertex out-degrees for all vertices in the graph g. VertexOutDegreegives the vertex out-degree for the vertex v.
• The vertex out-degree for a vertex v is the number of outgoing directed edges from v.
• For an undirected graph g, an edge is taken to be both an in-edge and an out-edge.
Find the out-degree for each vertex:
Find the out-degree for a specified vertex:
Find the out-degree for each vertex:
 Out[1]=

Find the out-degree for a specified vertex:
 Out[1]=
 Scope   (4)
VertexOutDegree works for directed graphs:
For undirected graphs, out-degree is taken to be the same as degree:
Vertex out-degree for a vertex:
Works with large graphs:
 Applications   (3)
Highlight the vertex by its vertex out-degree for CycleGraph:
Show the out-degree histogram for BernoulliGraphDistribution:
The out-degree distribution follows BinomialDistribution:
Create a food chain where an edge indicates what animals and insects eat:
The out-degree corresponds to the number of predators for the species:
Animals with zero out-degree are called top species or apex predators:
The out-degree of an undirected graph is the number of edges incident to each vertex:
Self-loops are counted twice:
Undirected graphs correspond to directed graphs with each edge both an in- and out-edge:
For an undirected graph, the vertex in-degree and out-degree are equal to the vertex degree:
For a directed graph, the sum of the vertex in-degree and out-degree is the vertex degree:
Put the vertex degree, in-degree, and out-degree before, above, and below the vertex, respectively:
The sum of the out-degrees of all vertices of an undirected graph is twice the number of edges:
The sum of the out-degrees of all vertices of a directed graph is equal to the number of edges:
A connected directed graph is Eulerian iff every vertex has equal in-degree and out-degree:
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