1. Degree Distribution Ralucca Gera,
Applied Mathematics Dept. Naval Postgraduate School Monterey, California

2. 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

3. 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

4. Plot of degree distribution random graph

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