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

# DegreeCentrality

 DegreeCentrality[g] gives a list of vertex degrees for the vertices in the underlying simple graph of g. DegreeCentralitygives a list of vertex in-degrees. DegreeCentralitygives a list of vertex out-degrees.
• The vertex degree for a vertex v is the number of edges incident to v.
• For a directed graph, the in-degree is the number of incoming edges and the out-degree is the number of outgoing edges.
• For an undirected graph, in-degree and out-degree coincide.
Find the degree for each vertex:
Find the in-degree and out-degree for each vertex:
Find the degree for each vertex:
 Out[1]=

Find the in-degree and out-degree for each vertex:
 Out[2]=
 Out[3]=
 Scope   (3)
DegreeCentrality for undirected graphs:
Directed graphs:
In-degree and out-degree:
Works with large graphs:
 Applications   (4)
Highlight the degree centrality for CycleGraph:
An unbalanced tree:
Label the vertex with in-degree and out-degree:
The degree is the sum of in- and out-degrees:
Vertex degrees of the HararyGraph:
Highlight and label the vertex by its degree:
Create a social network:
Find the people with more influence:
The degree of a vertex of an undirected graph is the number of edges incident to the vertex:
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 degrees of all vertices of a graph is twice the number of edges:
Every graph has an even number of vertices with odd degree:
Each vertex of a -regular graph has the same vertex degree :
All vertices of a simple graph have a maximum degree less than the number of vertices:
A simple graph without isolated vertices has at least one pair of vertices with equal degrees:
New in 8