Extremal linkage networks

TL;DR

This paper introduces extremal linkage networks, a new class of spatial networks generated by a reinforcement mechanism on layered graphs, where node fitness influences connectivity and results in complex, scale-free properties.

Contribution

It presents a novel model for spatial networks based on max-stable fitness distributions, explaining the emergence of small-world and scale-free features.

Findings

Complex spatial networks arise naturally from reinforcement mechanisms.

Max-stable fitness distributions lead to scale-free degree distributions.

The model explains the emergence of small distances in the network.

Abstract

We demonstrate how sophisticated graph properties, such as small distances and scale-free degree distributions, arise naturally from a reinforcement mechanism on layered graphs. Every node is assigned an a-priori i.i.d. fitness with max-stable distribution. The fitness determines the node attractiveness w.r.t. incoming edges as well as the spatial range for outgoing edges. For max-stable fitness distributions, we thus obtain complex spatial network, which we coin extremal linkage network.