Bose-Einstein Condensation in Networks

In 1924, Satyendra Nath Bose and Albert Einstein predicted that at extremely low temperatures, a macroscopic number of particles would collapse into the same quantum state, forming a new phase of matter—the Bose-Einstein condensate. In 2001, Ginestra Bianconi and Albert-László Barabási discovered that the same mathematical structure governs the dynamics of complex networks: when the fitness values of nodes in a growing network are distributed with sufficient inequality, the highest-fitness node can achieve a winner-take-all dominance, capturing a finite fraction of all the network’s connections—a condensation event. This is not merely metaphor. The mathematical equations governing the two phenomena are formally identical. And the condensation phenomenon explains events that pure preferential attachment cannot account for: the explosive, discontinuous rise of Google over AltaVista, of Facebook over Myspace, of the iPhone over Nokia. In each case, a node of exceptional fitness entered a market dominated by established hubs and captured a disproportionate share of connections with a speed that looked miraculous but was mathematically predicted.