gives the list of vertex in-degrees for all vertices in the graph g.
gives the vertex in-degree for the vertex v.
uses rules vw to specify the graph g.
- 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. »
Examplesopen allclose all
VertexInDegree works with directed graphs:
Vertex in-degree for a vertex:
Use rules to specify the graph:
VertexInDegree works with large graphs:
Highlight the vertex in-degree for directed graphs including CycleGraph:
Show the in-degree histogram for BernoulliGraphDistribution[n,p]:
The in-degree distribution follows BinomialDistribution[n-1,p]:
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:
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:
Wolfram Research (2010), VertexInDegree, Wolfram Language function, https://reference.wolfram.com/language/ref/VertexInDegree.html (updated 2015).
Wolfram Language. 2010. "VertexInDegree." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/VertexInDegree.html.
Wolfram Language. (2010). VertexInDegree. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/VertexInDegree.html