Two-level relationships and Scale-Free Networks

TL;DR

This paper introduces a new, efficient model for generating scale-free networks based on two-level relationships, which differs from traditional preferential attachment models and offers tunable degree distributions and clustering properties.

Contribution

The authors propose a novel, faster method for creating scale-free networks using real and virtual links, with adjustable degree exponents and distinct clustering characteristics.

Findings

The model produces scale-free networks with tunable degree exponents.

It is computationally more efficient than the Barabási-Albert model.

Reducing potential connection partners enhances network diversity.

Abstract

Through the distinction between ``real'' and ``virtual'' links between the nodes of a graph, we develop a set of simple rules leading to scale-free networks with a tunable degree distribution exponent. Albeit sharing some similarities with preferential attachment, our procedure is both faster than a na\"ive implementation of the Barab\'asi and Albert model and exhibits different clustering properties. The model is thoroughly studied numerically and suggests that reducing the set of partners a node can connect to is important in seizing the diversity of scale-free structures.