Degree distribution

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In the mathematical field of graph theory the degree distribution of a graph is a function describing the total number of vertices in a graph with a given degree (number of connections to other vertices).

Formally, the degree distribution is

[ p(k) = \sum_ 1 ]

where v is a vertex in the set of the graph's vertices V, and [\deg(v)] is the degree of vertex v.

This same information is often presented as the cumulative degree distribution,

[P_k = \sum_^ p_].

The degree distribution is a common way of classifying graphs into categories, such as Random graphs (Poisson distribution) and Scale-free networks (Power law distribution).

References

Newman, Mark E.J. ["The structure and function of complex networks"].

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