Local network growth: How simple rules drive network complexity
2026-08-03 • Social and Information Networks
Social and Information Networks
AI summaryⓘ
The authors explain that many different networks, like the Internet or social groups, look similar because they all grow using simple local rules rather than anyone planning the whole structure. Instead of new parts checking the entire network before connecting, each new node links based only on nearby connections. This local process naturally creates big hubs, tight clusters, and multiple paths, which are common features in real-world networks. The book shows how various systems develop their complex patterns through these simple, local steps.
networknodehublocal rulespreferential attachmentclusteringcomplex systemsnetworks growthcitation graphsocial networks
Authors
Alexei Vazquez
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.