The distribution of degree values \(d(u)\) over all vertices \(u\) characterizes the network as a whole, and is often used to visualize a network. In particular, a power law is often assumed, stating that the number of nodes with \(n\) neighbors is proportional to \(n^{-\gamma}\), for a constant \(\gamma\) [1]. This assumption can be inspected visually by plotting the degree distribution on a doubly logarithmic scale, on which a power law renders as a straight line.

The degree distribution shows the number of nodes with degree \(n\), in function of \(n\).

This plot uses a doubly logarithmic scale.