Universal fractal scaling of self-organized networks

TL;DR

This paper reveals that self-organized networks across biological, social, and technological domains follow a universal fractal power law relationship between size and connection density, indicating an optimal density pattern.

Contribution

It demonstrates a universal fractal scaling law governing the size and density of diverse self-organized networks, supported by empirical analysis of 47 networks.

Findings

Size and density follow a power law relationship

The relationship spans over 6 orders of magnitude

Indicates an optimal connection density in self-organized networks

Abstract

There is an abundance of literature on complex networks describing a variety of relationships among units in social, biological, and technological systems. Such networks, consisting of interconnected nodes, are often self-organized, naturally emerging without any overarching designs on topological structure yet enabling efficient interactions among nodes. Here we show that the number of nodes and the density of connections in such self-organized networks exhibit a power law relationship. We examined the size and connection density of 47 self-organizing networks of various biological, social, and technological origins, and found that the size-density relationship follows a fractal relationship spanning over 6 orders of magnitude. This finding indicates that there is an optimal connection density in self-organized networks following fractal scaling regardless of their sizes.