Thanks to ScienceWeek RANDOM GRAPH MODELS OF SOCIAL NETWORKS In mathematics, a "graph", in the context of the field known as "graph theory", is a mathematical object composed of points known as "vertices" or "nodes" and lines connecting some (possibly empty) subset of them, known as "edges". A "random graph", in this context, is a graph in which properties such as the number of nodes, edges, and connections between them are determined in some random way. ... ... M.E. Newman et al (Columbia University, US) discuss social networks, the authors making the following points: 1) A social network is a set of people or groups of people, "actors" in the jargon of the field, with some pattern of interactions or "ties" between them. Friendships among a group of individuals, business relationships between companies, and intermarriages between families are all examples of social networks that have been studied in the past. Network analysis has a long history in sociology, the literature on the topic stretching back at least half a century to the pioneering work of Rapoport, Harary, and others in the 1940s and 1950s. Typically, network studies in sociology have been data-oriented, involving empirical investigation of real-world networks, the investigation often followed by graph theoretical analysis aimed at determining the centrality or influence of the various actors. 2) Most recently, after a surge in interest in network structure among mathematicians and physicists, partly as a result of research on the Internet and on the World Wide Web, another body of research has investigated the statistical properties of networks and methods for modeling networks either analytically or numerically. One important and fundamental result that has emerged from these studies concerns the numbers of ties that actors have to other actors, their so-called "degrees". It has been found that in many networks, the distribution of actors' degrees is highly skewed, with a small number of actors having an unusually large number of ties. Simulations and analytical work have suggested that this skewness could have an impact on the way in which communities operate, including the way information travels through the network and the robustness of networks to removal of actors. 3) The authors describe some new exactly solvable models of the structure of social networks, the models based on random graphs with arbitrary degree distribution. The authors provide models both for simple unipartite networks, such as acquaintance networks, and for bipartite networks, such as affiliation networks. The authors compare the predictions of their models to data for a number of real-world social networks and find that in some cases the models are in remarkable agreement with the data, whereas in other cases the agreement is poorer, perhaps indicating the presence of additional social structure in the network not captured by the random graph. Proc. Nat. Acad. Sci. 2002 99:2566 Copyright (c) 1997-2002 ScienceWeek http://www.scienceweek.com *****************************|***************************** * * * BMS * * (Bulletin de Methologie Sociologique) * * (Bulletin of Sociological Methodology) * * [log in to unmask] * * http://www.ccr.jussieu.fr/bms * * * * RC33 * * (Research Committee "Logic & Methodology" * * of the International Sociological Association) * * [log in to unmask] * * http://local.uaa.alaska.edu/~aaso353/isa/index.htm * * * * Karl M. van Meter * * email [log in to unmask] LASMAS, IRESCO-CNRS * * tel/fax 33 (0)1 40 51 85 19 59 rue Pouchet * * 75017 Paris, France * * http://www.iresco.fr/labos/lasmas/accueil_f.htm * *****************************|*****************************