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

# VertexInDegree

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

Find the in-degree for a specified vertex:
 Out[1]=
 Scope   (4)
VertexInDegree works with directed graphs:
For undirected graphs, in-degree is taken to be the same as degree:
Vertex in-degree for a vertex:
Works with large graphs:
 Applications   (4)
Highlight the vertex in-degree for directed graphs including CycleGraph:
Show the in-degree histogram for BernoulliGraphDistribution:
The in-degree distribution follows BinomialDistribution:
The vertex in-degree distribution for PriceGraphDistribution follows a power-law:
Create a food chain where an edge indicates what animals and insects eat:
The in-degree corresponds to the number of prey and what an animal preys on:
The species with in-degree zero are called basal species or producers:
The in-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 in-degrees of all vertices of an undirected graph is twice the number of edges:
The sum of the in-degrees of all vertices of a directed graph is equal to the number of edges:
The vertex in-degrees of an undirected graph can be obtained from the adjacency matrix:
The vertex in-degrees of a directed graph can be obtained from the adjacency matrix:
The vertex in-degrees for an undirected graph can be obtained from the incidence matrix:
A connected directed graph is Eulerian iff every vertex has equal in-degree and out-degree:
New in 8