Scale-free network growth by ranking

TL;DR

This paper introduces a new network growth model based on node rankings rather than exact prestige values, explaining the emergence of scale-free networks even with partial information.

Contribution

It proposes a ranking-based growth criterion that results in scale-free networks, applicable to various prestige measures and explaining real-world network properties.

Findings

Scale-free degree distribution emerges from ranking-based linking.

The model applies even with partial rank information.

Illustrated with Web graph as a case study.

Abstract

Network growth is currently explained through mechanisms that rely on node prestige measures, such as degree or fitness. In many real networks those who create and connect nodes do not know the prestige values of existing nodes, but only their ranking by prestige. We propose a criterion of network growth that explicitly relies on the ranking of the nodes according to any prestige measure, be it topological or not. The resulting network has a scale-free degree distribution when the probability to link a target node is any power law function of its rank, even when one has only partial information of node ranks. Our criterion may explain the frequency and robustness of scale-free degree distributions in real networks, as illustrated by the special case of the Web graph.