The small-world effect is a modern phenomenon

The “small-world effect” is the observation that one can find a short chain of acquaintances, often of no more than a handful of individuals, connecting almost any two people on the planet. It is often expressed in the language of networks, where it is equivalent to the statement that most pairs of individuals are connected by a short path through the acquaintance network. Although the small-world effect is well-established empirically for contemporary social networks, we argue here that it is a relatively recent phenomenon, arising only in the last few hundred years: for most of mankind’s tenure on Earth the social world was large, with most pairs of individuals connected by relatively long chains of acquaintances, if at all. Our conclusions are based on observations about the spread of diseases, which travel over contact networks between individuals and whose dynamics can give us clues to the structure of those networks even when direct network measurements are not available. As an example we consider the spread of the Black Death in 14th-century Europe, which is known to have traveled across the continent in well-defined waves of infection over the course of several years. Using established epidemiological models, we show that such wave-like behavior can occur only if contacts between individuals living far apart are exponentially rare. We further show that if long-distance contacts are exponentially rare, then the shortest chain of contacts between distant individuals is on average a long one. The observation of the wave-like spread of a disease like the Black Death thus implies a network without the small-world effect.

💡 Research Summary

The paper “The small‑world effect is a modern phenomenon” puts forward the provocative claim that the small‑world property—characterized by short average path lengths that grow at most logarithmically with population size—did not exist for most of human history and only emerged in the last few centuries. Because direct measurements of pre‑industrial social networks are unavailable, the authors turn to historical epidemic patterns as indirect probes of the underlying contact structure.

The authors begin by reviewing the modern literature on small‑world networks, from the early theoretical work of Pool and Kochen through Milgram’s “six degrees of separation” experiments, to the Watts‑Strogatz model and recent analyses of human mobility that reveal power‑law distributions of travel distances. In contemporary societies these long‑range links, even if sparse, are sufficient to shrink the network diameter to logarithmic scales, producing the familiar “small‑world” effect.

Turning to the past, the paper focuses on the 14th‑century Black Death, which spread across Europe from 1347 to 1350 at an approximately constant speed of 800 km per year, forming a clear wave‑front that moved northward and eastward in a roughly concentric fashion. This wave‑like progression contrasts sharply with modern epidemics that can appear almost simultaneously in distant locations due to rapid air travel.

To formalize the relationship between epidemic spread and contact topology, the authors adopt a non‑local susceptible–infectious (SI) model introduced by Mollison. They define a distance‑dependent contact kernel α(r), representing the per‑unit‑time probability that two individuals separated by distance r have a contact sufficient for disease transmission. The kernel is assumed isotropic, translation‑invariant, and non‑increasing beyond some finite radius. The dynamics of the infection probability P(u,t) obey the integro‑differential equation

∂ₜP(u,t)=