The fractal/small-world dichotomy in real-world networks

TL;DR

This paper identifies a fundamental dichotomy in real-world networks, distinguishing between small-world networks with exponential growth and fractal networks with power-law growth, influenced by degree correlations and geography.

Contribution

It highlights the existence of a clear dichotomy in network structures and explores factors influencing this distinction, such as degree correlations and geographical constraints.

Findings

Small-world networks exhibit exponential neighborhood growth.

Fractal networks display power-law neighborhood growth.

The status of human social networks in this dichotomy remains uncertain.

Abstract

We draw attention to a clear dichotomy between small-world networks exhibiting exponential neighborhood growth, and fractal-like networks where neighborhoods grow according to a power law. This distinction is observed in a number of real-world networks, and is related to the degree correlations and geographical constraints. We conclude by pointing out that the status of human social networks in this dichotomy is far from clear.