Local versus Global Knowledge in the Barabasi-Albert scale-free network model

TL;DR

This paper investigates how local versus global knowledge in the Barabasi-Albert model affects network properties, showing that some global features are robust to local knowledge while others align more with real-world networks.

Contribution

It introduces a variant of the BA model applying preferential attachment locally, revealing which network properties depend on global versus local information.

Findings

Global properties like degree distribution are robust to local knowledge.

Local properties such as clustering coefficient differ from the original model.

Some properties approach real-world network measurements with local attachment.

Abstract

The scale-free model of Barabasi and Albert gave rise to a burst of activity in the field of complex networks. In this paper, we revisit one of the main assumptions of the model, the preferential attachment rule. We study a model in which the PA rule is applied to a neighborhood of newly created nodes and thus no global knowledge of the network is assumed. We numerically show that global properties of the BA model such as the connectivity distribution and the average shortest path length are quite robust when there is some degree of local knowledge. In contrast, other properties such as the clustering coefficient and degree-degree correlations differ and approach the values measured for real-world networks.