Algorithms and Models for the Web-Graph: 7th International by Ravi Kumar, D Sivakumar

By Ravi Kumar, D Sivakumar

This publication constitutes the refereed lawsuits of the seventh foreign Workshop on Algorithms and types for the Web-Graph, WAW 2010, held in Stanford, CA, united states, in December 2010, which used to be co-located with the sixth overseas Workshop on net and community Economics (WINE 2010). The thirteen revised complete papers and the invited paper provided have been conscientiously reviewed and chosen from 19 submissions.

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Additional info for Algorithms and Models for the Web-Graph: 7th International Workshop, WAW 2010, Stanford, CA, USA, December 13-14, 2010, Proceedings

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In the random intersection graph (RIG) model, nodes have certain attributes with fixed probabilities. In this paper, we have considered the general RIG model, where these probabilities are represented by a set of probabilities p = {pw : w ∈ W }, where pw denotes the probability that a node is attached to the attribute w. We have analyzed the evolution of components in general RIGs, giving conditions for existence and uniqueness of the giant component. We have done so by generalizing the branching process argument used to study the birth of the giant component in Erd˝os-R´enyi graphs.

We now focus on describing the distribution of φt = α∈Wt qα . For t ≥ 0, we have t φt = d qα = α∈Wt t I(Γw =j) qw = qα = j=0 α∈Wj \Wj−1 j=0 w∈W I(Γw ≤t) qw . t+1 1 − (1 − qw )(1 − qw ) . E[φt ] = (15) w∈W (16) w∈W The concentration of φ0 will be crucial for the analysis of the supercritical regime. Hence, we provide E[φ0 ] and E[φ20 ] here. 2, we will assume that pw = p(log n/n). Under this condition, it follows from (16) that (1 − p2w ) = 1 − E[φ0 ] = w∈W p2w + o( w∈W w∈W p2w ). (17) 42 M. Bradonji´c et al.

Business, family, friendships) or the means of This work is supported by the Laboratory Directed Research and Development program of Sandia National Laboratories. This author is also supported by DOE Applied Mathematics Research Program. S. Department of Energys National Nuclear Security Administration under contract DE-AC04-94AL85000. R. Kumar and D. ): WAW 2010, LNCS 6516, pp. 25–35, 2010. c Springer-Verlag Berlin Heidelberg 2010 26 M. Rocklin and A. , emails, phone, in person). Electronic files can be grouped by their type (Latex, C, html), names, the time they are created, or the pattern they are accessed.

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