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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.

Degree distribution

Outdegree distribution

Indegree distribution

Left degree distribution

Right degree distribution