April 20, 2017

Download Algorithms and Models for the Web-Graph: 7th International by Andrei Broder (auth.), Ravi Kumar, Dandapani Sivakumar PDF

By Andrei Broder (auth.), Ravi Kumar, Dandapani Sivakumar (eds.)

This e-book constitutes the refereed court cases 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 was once co-located with the sixth overseas Workshop on web 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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A well-known example is a collaboration graph, where the two sets might be scientists and research papers, or actors and movies [27,18]. Simulations of epidemic spread in human populations are often performed on networks constructed from bipartite graphs of people and the locations they R. Kumar and D. ): WAW 2010, LNCS 6516, pp. 36–49, 2010. c Springer-Verlag Berlin Heidelberg 2010 Component Evolution in General Random Intersection Graphs 37 visit during a typical day [11]. Bipartite structure is hardly limited to social networks.

However, modeling such networks remains a challenge. The wellstudied Erd˝os-R´enyi model, Gn,p , successfully used for average-case analysis of algorithm performance, does not satisfactorily represent many randomly formed social or collaboration networks. Gn,p does not capture the typical scale-free degree distribution of many real-world networks [3]. More realistic degree distributions can be achieved by the configuration model [20] or expected degree model [7], but even those fail to capture common properties of social networks such as the high number of triangles (or cliques) and strong degree-degree correlation [19,1].

Finally, the union bound over the n possible starting values v0 gives P[max T (v0 ) > K4 log n] ≤ no(n−1 ) = o(1), v0 ∈V which implies that all connected components are of size O(log n), whp. 2 Supercritical Regime We now turn to the study of the supercritical regime in which limn→∞ n c > 1. w∈W p2w = Component Evolution in General Random Intersection Graphs 45 Theorem 2. Suppose that pw = o log n n for all w p3w = o and w∈W log n . n2 For any constant c > 1, if w∈W p2w = c/n, then whp there exists a unique largest component in G(n, m, p), of order Θ(n).

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