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## Degree distribution

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.

 [1] Albert-László Barabási and Réka Albert. Emergence of scaling in random networks. Science, 286(5439):509-512, 1999.