Compute degree centralities:

Highlight:

Rank vertices. Highest-ranked vertices have the most connections to other vertices:

DegreeCentrality works with undirected graphs:

Directed graphs:

Multigraphs:

Mixed graphs:

Use rules to specify the graph:

Compute in-degree and out-degree:

DegreeCentrality works with large graphs:

Rank vertices by their influence on other vertices in their immediate neighborhood:

Highlight the degree centrality for CycleGraph:

GridGraph:

CompleteKaryTree:

PathGraph:

A friendship network in a school. Find the most popular students:

A citation network from the High Energy Physics Phenomenology section of the arXiv e-Print archive. Find the top 10 most-cited articles:

Find the basal species or producers in a food chain:

Find the top species or apex predators:

A network of email sent to the MathGroup list in November 2011. Construct a social network of users, with an edge from to if has sent at least one reply to . Find the users who are the most active at answering questions:

Count the users who only received replies and did not send any replies:

Find the users who asked questions most often:

Count the users who only sent replies and did not receive any replies:

The internet at the level of autonomous systems. The frequency of the degree centrality follows a power-law distribution:

Obtain the maximum likelihood parameter estimates, assuming a Zipf distribution:

Probability density function:

For graphs with vertices, the largest sum in differences in degree centrality between the most central vertex and all other vertices is :

Measure how central the most central vertex is with respect to other vertices:

Centralization of social networks:

The degree of a vertex of an undirected graph is the number of edges incident to the vertex:

For an undirected graph, the in-degree and out-degree centralities coincide:

Use VertexDegree to obtain the degree of a specific vertex:

DegreeCentrality is equivalent to VertexDegree for simple graphs:

For a directed graph, the sum of in- and out-degree centralities is equal to the vertex degree: