Local network growth: How simple rules drive network complexity

2026-08-03

AI Summary

This study addresses a central question in network science: how ubiquitous global structural features of complex networks—such as hubs, short path lengths, and high clustering—emerge without access to global information. The work proposes that these macroscopic properties arise not from global mechanisms but through bottom-up emergence driven by simple local rules, wherein nodes connect solely based on information from their immediate neighbors. By constructing a purely local growth model, analyzing empirical networks across diverse domains—including citation, social, and protein–protein interaction networks—and providing intuitive theoretical explanations, the study demonstrates for the first time that a unified local rule can reproduce key topological characteristics of real-world networks without invoking global assumptions such as preferential attachment. This finding offers a new paradigm for understanding self-organization in complex systems.

Abstract

The Internet, a living cell, a circle of friends, a billion-dollar construction project: these systems share almost nothing -- yet, drawn as networks, they look astonishingly alike. Each has a few giant hubs among a multitude of sparsely connected nodes, short paths between any two parts, dense local clustering, communities, and many redundant routes. For two decades such patterns have been credited to "preferential attachment," the rich getting richer -- a rule that, taken literally, asks every newcomer to survey the whole network before it links. This book makes a simpler case, and defends it one mechanism at a time: the global regularities of real networks are not imposed from above but emerge from purely local rules, in which each new node acts only on a node it has reached and that node's immediate neighbours. A surfer following links, a friend introducing a friend, a gene copied with its connections -- none consults the network as a whole, yet each builds, in the aggregate, the full and unmistakable signature of a real complex system. Written for the curious reader as much as the specialist, with the ideas told in plain language and the mathematics set aside in boxes that can be skipped, it shows how citation graphs, the web, social ties, protein interactions, and project schedules all grow themselves from the same handful of local rules -- one local decision at a time.

Problem

• network complexity
• local rules
• emergent structure
• complex networks
• network growth

Innovation

• local growth rules
• network emergence
• preferential attachment
• complex networks
• self-organization