Atypical scaling behavior persists in real world interaction networks

TL;DR

This paper reveals that real-world interaction networks often exhibit a scale-free power law with an exponent between 1 and 2, challenging previous assumptions and providing a new generative model for this atypical behavior.

Contribution

It introduces a generative model explaining the atypical scale-free behavior with exponents between 1 and 2 in real-world networks, supported by empirical data and theoretical analysis.

Findings

Empirical networks often have power law exponents between 1 and 2.

A new generative model explains this atypical scaling behavior.

The model incorporates constant edge growth and positive feedback mechanisms.

Abstract

Scale-free power law structure describes complex networks derived from a wide range of real world processes. The extensive literature focuses almost exclusively on networks with power law exponent strictly larger than 2, which can be explained by constant vertex growth and preferential attachment. The complementary scale-free behavior in the range between 1 and 2 has been mostly neglected as atypical because there is no known generating mechanism to explain how networks with this property form. However, empirical observations reveal that scaling in this range is an inherent feature of real world networks obtained from repeated interactions within a population, as in social, communication, and collaboration networks. A generative model explains the observed phenomenon through the realistic dynamics of constant edge growth and a positive feedback mechanism. Our investigation, therefore, yields a novel empirical observation grounded in a strong theoretical basis for its occurrence.