Networks: A Very Short Introduction by Guido Caldarelli & Michele Catanzaro

Author:Guido Caldarelli & Michele Catanzaro [Caldarelli, Guido & Catanzaro, Michele]
Language: eng
Format: epub
ISBN: 9780199588077
Publisher: Oxford University Press
Published: 2012-12-15T06:00:00+00:00

Looking at the degree distribution is the best way to check if a network is heterogeneous or not: if the distribution is fat tailed, then the network will have hubs and heterogeneity. A mathematically perfect power law is never found, because this would imply the existence of hubs with an infinite number of connections. However, no real network is infinitely big: this is why the fat tail of the degree distribution always has a cut-off at a maximum value for the degree. Indeed, the size of hubs can be limited by various costs of accumulating connections: for example, neurons cannot accumulate an arbitrary amount of connections, because of their physical structure. In professional collaboration networks, time plays a role: connections cannot be accumulated indefinitely, because at a certain moment the career (or life) of an individual comes to an end. All these and other factors are reflected in the shape of the degree distribution. Nonetheless, a strongly skewed, fat-tailed distribution is a clear signal of heterogeneity, even if it is never a perfect power law.

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