New arXiv book: local rules, not preferential attachment, drive network complexity

For twenty years, network scientists have credited the striking resemblance between the Internet, cellular networks, and social graphs to preferential attachment—the idea that new nodes connect to highly connected hubs, making the rich richer. But that rule implies every newcomer surveys the entire network before linking, which is both unrealistic and computationally expensive. In a new 215-page book posted to arXiv (paper 2608.01853), physicist Alexei Vazquez makes a simpler case: global network structure emerges from purely local rules. Each new node only interacts with the node it reaches and that node's immediate neighbors—no global knowledge required.

Vazquez draws on concrete examples: a web surfer following links, a friend introducing a friend, or a gene duplicating with its connections. None consults the whole network, yet all produce the same signature: a few hubs, short paths, dense clustering, communities, and redundant routes. The book, written for general readers with mathematics isolated in skippable boxes, systematically demonstrates how citation graphs, the web, social ties, protein interactions, and billion-dollar construction projects all self-assemble from the same handful of local rules. It directly challenges the preferential attachment orthodoxy, offering a unified, local-growth alternative that may reshape how researchers model everything from epidemic spread to infrastructure design.