A remark on the BA model of scale-free networks

TL;DR

This paper introduces a modified BA model with a regulatory parameter to better explain the power-law degree distributions observed in real-world scale-free networks, including links not originating from new nodes.

Contribution

A new modified BA model with a regulatory parameter and a master equation approach that better captures the empirical degree distribution of scale-free networks.

Findings

The modified model produces power-law degree distributions with exponents between two and three.

The regulatory parameter influences the growth rate of links in the network.

The master equation approach confirms the degree distribution results.

Abstract

The degree distributions of many real world networks follow power-laws whose exponents tend to fall between two and three. Within the framework of the Barabasi-Albert model (BA model), we explain this empirical observation by a simple fact. To that end we propose a modified BA model with one parameter that serves as a regulatory factor for the growth rate of added links in scale-free networks. The regulatory factor has something to do with the obvious fact that one link has two nodes. The modified model also allows to connect nodes by newly added links that do not necessarily emanate from new nodes. Another related model using the master equation is also given, from which the same power-law degree distribution can be derived.