Scale-free networks revealed from finite-size scaling

Complexity Digest

Networks play a vital role in the development of predictive models of physical, biological, and social collective phenomena. A quite remarkable feature of many of these networks is that they are believed to be approximately scale free: the fraction of nodes with k incident links (the degree) follows a power law p(k)∝k−λ for sufficiently large degree k. The value of the exponent λ as well as deviations from power law scaling provide invaluable information on the mechanisms underlying the formation of the network such as small degree saturation, variations in the local fitness to compete for links, and high degree cutoffs owing to the finite size of the network. Indeed real networks are not infinitely large and the largest degree of any network cannot be larger than the number of nodes. Finite size scaling is a useful tool for analyzing deviations from power law behavior in the vicinity of a…

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