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

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 used to be co-located with the sixth foreign Workshop on web and community Economics (WINE 2010).

The thirteen revised complete papers and the invited paper offered have been conscientiously reviewed and chosen from 19 submissions.

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Extra resources 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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Bradonji´c et al. such a process is complicated by the dependence on its history, dictated by the structure of general RIGs. We have shown that in spite of this difficulty, it is possible to give stochastic bounds on the branching process, and that under certain conditions the giant component appears at the threshold n w∈W p2w = 1, with probability tending to one, as the number of nodes tends to infinity. Acknowledgments Part of this work was funded by the Department of Energy ASCR program, by the Air Force Office of Scientific Research MURI grant FA9550-10-1-0569, and by the Office of Naval Research grant N00014-10-1-0641.

While additional constraints may exclude this specific solution, a linear formulation of the quality will always yield only a trivial solution within the new feasible region. In our experiments we used the modularity metric [9]. The modularity metric uses a random graph generated with respect to the degree distribution as the null hypothesis, setting the modularity score of a random clustering to 0. Formally, the modularity score for an unweighted graph is 1 2m eij − ij di dj δij , 4m (4) where eij is a binary variable that is 1, if and only if vertices vi and vj are connected; di denotes the degree of vertex i; m is the number of edges; and δi,j is a binary variable di dj that is 1, if and only if vertices vi and vj are on the same cluster.

2(3K1 + K2 ) Taking ν ∈ (0, 1 − c ) and t = K3 log n for some constant K3 large enough and not depending on the initial node v0 , we conclude that P[1−φt−1 ≥ (1−ν)t/n] = o(n−1 ), which in turn implies that taking constant K4 = max{K0 , K3 }, ensures that P[T (v0 ) > K4 log n] = o(1/n) for any initial node v0 . 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.

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