Extremal linkage networks (Q2135579)

In this article, the authors illustrate that classical methods from extreme value theory such as max-stable distributions have a major impact in analysis of complex networks with spatial structure such as social networks, electrical networks, the world-wide web, and others. Defining the extremal linkage network as a random layered network, where the node \(i \in \{0, \ldots, N-1\}\) in layer \(h \in \mathbb{Z}\) has a fitness \(F_{i,h},\) an i.i.d. family, the authors identify the asymptotic degree and distance distribution as \(N \rightarrow \infty.\) The results obtained show that scale-free and small world behaviour is present for Pareto fitness distributions with parameter at most 1. Detailed proofs are given in the article.