Degree Distribution Ralucca Gera,

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Presentation transcript:

Degree Distribution Ralucca Gera, Applied Mathematics Dept. Naval Postgraduate School Monterey, California rgera@nps.edu

Degree distributions The degree distribution is a frequency distribution of the degree sequence We define pk to be the fraction of vertices in a network that have degree k That is the same as saying: pk is the probability that a randomly selected node of the network will have degree k A well connected vertex is called a hub

Plot of the degree distribution The Internet Commonly seen plots of real networks Right-skewed Many nodes with small degrees, few with extremely high Largest degree is 2407 (not shown). Since 𝑛=19956 this node is adjacent to 12% of the network

Plot of degree distribution random graph

Degree distribution in directed networks For directed networks we have both in- and out-degree distributions The Web