Observed Degree Distributions
The degree distribution is very important in studying both real networks, such as the Internet and social networks, and theoretical networks. The simplest network model, for example, the (Bernoulli) random graph, in which each of n nodes is connected (or not) with independent probability p (or 1 − p), has a binomial distribution of degrees:
(or Poisson in the limit of large n). Most networks in the real world, however, have degree distributions very different from this. Most are highly right-skewed, meaning that a large majority of nodes have low degree but a small number, known as "hubs", have high degree. Some networks, notably the Internet, the world wide web, and some social networks are found to have degree distributions that approximately follow a power law: P(k) ~ k−γ, where γ is a constant. Such networks are called scale-free networks and have attracted particular attention for their structural and dynamical properties.
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