Revisiting ‘‘scale-free’’ networks

Problems and paradigmsRevisiting ‘‘scale-free’’ networksEvelyn Fox Keller*Summary later makes explicit (the term ‘‘scale-free’’, he explains, is ‘‘a(5)Recent observations of power-law distributions in the name that is rooted in statistical physics literature’’), theyconnectivityofcomplexnetworkscameasabigsurpriseargue that the finding of a power law distribution ‘‘indicates thatto researchers steeped in the tradition of random net-(2)large networks self-organize into a scale-free state’’. Theworks. Even more surprising was the discovery thatbasic hypothesis of their model was that, as new connectionspower-law distributions also characterize many biologi-cal and social networks. Many attributed a deep signifi- form, they attach to a node with a probability proportional tocance to this fact, inferring a ‘‘universal architecture’’ of the existing number of connections (growth and preferentialcomplex systems. Closer examination, however, chal-attachment). In other words, the rich get richer, a processlenges the assumptions that (1) such distributions are(6)otherwise known as the ‘‘Matthew effect’’. In addition tospecial and (2) they signify a common architecture, in-dependentofthesystem’sspecifics.Therealsurprise,if generating distributions resembling those observed for theany,isthatpower-lawdistributionsareeasytogenerate, Web, Baraba ´si and Albert also suggested that ‘‘Growth andand by a variety of mechanisms. The architecture that preferential attachment ...