Duncan Watts and Albert-Lรกszlรณ Barรกbasi are the both physicists who have recently crashed the world of social networks, arousing some resentment in the process. Both have made a splash in the wider scientific community, as attested by their publications in high status science journals (Science, Nature). Both have analyzed some of the same very large networks (for example, the internet). Both use models from physics-Bose-Einstein condensation, percolation, and so on. Both have recently written scientific best-sellers: Six Degrees ranks 2547 on the Amazon list, while Linked ranks 4003. These similarities, however, obscure profound and important differences between the two models they initiated. Watts and Barรกbasi had different purposes in creating their models, and the models are applicable in different situations.
First, let me lay out the actors in this drama. The mathematician Paul Erdลs and his colleague Alfrรฉd Rรฉnyi played an important role in developing the model of a random graph 1 a graph in which either a fixed number of edges are randomly distributed among all the pairs of a set of nodes, or, alternatively, a graph in which every pair have the same independent probability of being connected (Bollabรกs, 2001). This mathematically tractable but completely unrealistic model has been used as a baseline in epidemiology and other fields. Random networks completely lack structure: there is no tendency to form clusters (cliques); actors do not differ in their propensities to form contacts; there are no tendencies for centralization or transitivity. In fact, no conceivable bias exists in random graphs-no leadership, no homophily of choice-no nothing. Compared to actual social networks, random graphs have a low level of clustering (no cliquing), small differences in degree among the vertices, and short distances between vertices. In exchange for this unrealistic simplicity, we can calculate other important features of networks such as the distribution of component sizes and average distances between nodes. Duncan Watts's brilliance was in framing an excellent question: if Stanley Milgram's well-known "small world" experiment is correct, real social networks have two incompatible Watts, D.J., 1999. Small worlds: The Dynamics of Networks between Order and randomness.