Recent observations of power-law distributions in the connectivity of complex networks came as a big surprise to researchers steeped in the tradition of random networks. Even more surprising was the discovery that power-law distributions also characterize many biological and social networks. Many attributed a deep significance to this fact, inferring a “universal architecture” of complex systems. Closer examination, however, challenges the assumptions that (1) such distributions are special and (2) they signify a common architecture, independent of the system's specifics. The real surprise, if any, is that power-law distributions are easy to generate, and by a variety of mechanisms. The architecture that results is not universal, but particular; it is determined by the actual constraints on the system in question. BioEssays 27:1060–1068, 2005. © 2005 Wiley Periodicals, Inc.