BUILT-IN MATHEMATICA SYMBOL

VertexInDegree

VertexInDegree[g]
gives the list of vertex in-degrees for all vertices in the graph g.

VertexInDegree

gives the vertex in-degree for the vertex v.

MORE INFORMATION

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.

EXAMPLES

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Basic Examples (2)

Find the in-degree for each vertex:

Find the in-degree for a specified vertex:

Find the in-degree for each vertex:

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Find the in-degree for a specified vertex:

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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:

Properties & Relations (10)

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: