By Evimaria Terzi, Marco Winkler (auth.), Alan Frieze, Paul Horn, Paweł Prałat (eds.)
This ebook constitutes the refereed lawsuits of the eighth overseas Workshop on Algorithms and types for the Web-Graph, WAW 2011, held in Atlanta, GA, in may well 2011 - co-located with RSA 2011, the fifteenth foreign convention on Random buildings and Algorithms.
The thirteen revised complete papers provided including 1 invited lecture have been rigorously reviewed and chosen from 19 submissions. Addressing a large choice of themes with regards to the learn of the Web-graph reminiscent of theoretical and empirical research, the papers characteristic unique learn by way of algorithmic and mathematical research in all parts bearing on the World-Wide internet with precise concentration to the view of advanced facts as networks.
Read or Download Algorithms and Models for the Web Graph: 8th International Workshop, WAW 2011, Atlanta, GA, USA, May 27-29, 2011. Proceedings PDF
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Extra info for Algorithms and Models for the Web Graph: 8th International Workshop, WAW 2011, Atlanta, GA, USA, May 27-29, 2011. Proceedings
During 100 runs of the algorithm, 99 of them return such an (α, β)-community that signiﬁcantly overlaps with one core but is disjoint from the other. 22% of the other core B. However, no other intermediate (α, β)-communities can be found between B and C using the above method, which demonstrates the non-existence of a bridge. Detecting the Structure of Social Networks Using (α, β)-Communities 35 Table 2. Cores of the Slashdot graph k 30 40 50 60 70 80 90 100 150 200 250 number of cores 29 10 3 3 3 3 3 3 2 1 1 average core size 25 33 41 53 62 72 85 97 148 197 244 Another approach to ﬁnding a bridge is to search for (α, β)-communities that fall between cores.
Xr−1 , x1 . Since dx = dx , Q and T commute, we have (T −1/2 BT −1/2 ) (T −1/2 BT −1/2 ) = T −1/2 B T −1 BT −1/2 = T −1/2 A Q T −1 QAT −1/2 = T −1/2 A T −1 Q QAT −1/2 = T −1/2 A T −1 AT −1/2 . Here we use the fact Q Q = I. This identity means that the singular values of I − L(r−1) is precisely equal to 1 minus the Laplacian eigenvalues of the graph G. Our deﬁnitions of Laplacians L(s) seem to be related to the quasi-randomness [7, 17] of hypergraphs. We are very interested in this direction.
Both the translation of this intuition into a welldefined mathematical formula and design of associated algorithms pose big challenges. Despite the high quality and the high volume of the literature, the area continues to draw a lot of interest due to the growing importance of the problem and the challenges posed by the size and mathematical variety of the subject graphs. Our goal here is to extend the concept of clustering to graphs with multiple edge types without getting into the details of clustering algorithms and formulations, since such a detailed study will be well beyond the scope of this paper.