Showing papers by "Duncan J. Watts published in 2001"
TL;DR: It is demonstrated that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world, while in others there is a measurable discrepancy between theory and reality, perhaps indicating the presence of additional social structure in the network that is not captured by the random graph.
Abstract: Recent work on the structure of social networks and the internet has focused attention on graphs with distributions of vertex degree that are significantly different from the Poisson degree distributions that have been widely studied in the past. In this paper we develop in detail the theory of random graphs with arbitrary degree distributions. In addition to simple undirected, unipartite graphs, we examine the properties of directed and bipartite graphs. Among other results, we derive exact expressions for the position of the phase transition at which a giant component first forms, the mean component size, the size of the giant component if there is one, the mean number of vertices a certain distance away from a randomly chosen vertex, and the average vertex-vertex distance within a graph. We apply our theory to some real-world graphs, including the worldwide web and collaboration graphs of scientists and Fortune 1000 company directors. We demonstrate that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world, while in others there is a measurable discrepancy between theory and reality, perhaps indicating the presence of additional social structure in the network that is not captured by the random graph.
3,655 citations
TL;DR: The dynamics of networks between order and randomness, characteristics of small world networks, and the structure and dynamic of networks mark newman.
Abstract: small worlds the dynamics of networks between order and. download small worlds the dynamics of networks between. small worlds and the dynamics of networks. small world networks oxford handbooks. small worlds the dynamics of networks between order and. small worlds the dynamics of networks between order and. book review small worlds the dynamics of networks. small worlds the dynamics of networks between order and. small worlds the dynamics of networks between order and. networks dynamics and the small world phenomenon. small world networks math insight. grossman oakland edu the american mathematical monthly. small world network. small world networks cs brynmawr edu. characteristics of small world networks. small worlds the dynamics of networks between order and. watts d j 1999 small worlds the dynamics of networks. small worlds the dynamics of networks between order and. ef?cient behavior of small world networks. small worlds the dynamics of networks between order and. the structure and dynamics of networks mark newman. small worlds the dynamics of networks between order and. small worlds the dynamics of networks between order and randomness. small worlds the
1,218 citations
01 Jan 2001
TL;DR: In this paper, the authors present a possible explanation of large but rare cascades in terms of a network of interacting agents whose decisions are determined by the actions of their neighbors, and identify conditions under which the network is susceptible to very rare, but very large cascades and explain why such cascades may be difficult to anticipate in practice.
Abstract: The origin of large but rare cascades that are triggered by small initial shocks is a problem that manifests itself in social and natural phenomena as diverse as cultural fads and business innovations (1–5), social movements and revolutions (6–8), and even cascading failures in large infrastructure networks (9–11). Here we present a possible explanation of such cascades in terms of a network of interacting agents whose decisions are determined by the actions of their neighbors. We identify conditions under which the network is susceptible to very rare, but very large cascades and explain why such cascades may be difficult to anticipate in practice.
27 citations