By Guido Caldarelli
This ebook is the end result of 3 years of study attempt on a multidisciplinary undertaking within which physicists, mathematicians, laptop scientists and social scientists labored jointly to reach at a unifying photo of advanced networks. The contributed chapters shape a reference for a number of the difficulties in information research visualization and modeling of complicated networks.
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Extra info for Large scale structure and dynamics of complex networks: from information technology to finance and natural science
Sample text
This is unlikely to be realistic, casting a shadow on a direct interpretation of the PA rule. In the next section a different model will be presented, likely to capture some real process behind the formation of the WWW and of protein interaction networks, in which preferential attachment emerges as an effective law from microscopic rules where only a local knowledge of the network is needed. 2. Duplication-divergence models It has been argued that some networks could be modeled by a growth process where new nodes are generated as copies of older ones.
Yet, since new proteins arising by this mechanism still share many physicochemical properties with their ancestors, many of their interactions remain unchanged, with the loss of some old and the acquisition of some new June 6, 2007 9:49 WSPC/Trim Size: 9in x 6in for Review Volume Models of Complex Networks book 29 ones. Extensive numerical simulations of such models have shown that the resulting networks are scale-free, or at least heavy-tailed. The duplication-divergence model is governed by a local rule, where no global knowledge of the network is needed.
2. 18 In this case to every nodes is assigned an integer index i (i = 1, . . , N ) and a weight pi = i−α , with 0 ≤ α < 1 uniform over the network. Pairs of nodes (i, j) are extracted at random with probabilities proportional, for each node, to its weight, pi / k pk and pj / k pk and they are joined by an edge, unless they already are. A total of mN nodes are added, for an average degree of 2m. The degree of a node in this model is the number of times it has been picked, which in turn is proportional to its weight.