By Jeannette Janssen, Paweł Prałat, Rory Wilson (auth.), Anthony Bonato, Michael Mitzenmacher, Paweł Prałat (eds.)

This e-book constitutes the refereed lawsuits of the tenth overseas Workshop on Algorithms and versions for the internet Graph, WAW 2013, held in Cambridge, MA, united states, in December 2013. The 17 papers provided have been rigorously reviewed and chosen for inclusion during this quantity. They tackle themes with regards to graph-theoretic and algorithmic features of comparable complicated networks, together with quotation networks, social networks, organic networks, molecular networks and different networks coming up from the Internet.

**Read or Download Algorithms and Models for the Web Graph: 10th International Workshop, WAW 2013, Cambridge, MA, USA, December 14-15, 2013, Proceedings PDF**

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An open triangle of Gt with tip x is simply a subgraph of the form ({x, y, z}, {{x, y}, {x, z}}), where y and z could either be connected in Gt and hence form a triangle, or not. Note that every triangle in G contributes three open triangles. The global clustering coeﬃcient of G is deﬁned as cglob (Gt ) := 3 Number of triangles included in Gt . Number of open triangles included in Gt Note that always cglob (Gt ) ∈ [0, 1]. The local clustering coeﬃcient of Gt at a vertex x with degree at least two is deﬁned by cloc x (Gt ) := Number of triangles included in Gt containing vertex x , Number of open triangles with tip x included in Gt which is also an element of [0, 1].

Probab. 13, 277–303 (2003) 20. : Random trees and general branching processes. edu Abstract. We give a clustering algorithm for connection graphs, that is, weighted graphs in which each edge is associated with a d-dimensional rotation. e. that have small edge boundary and the rotations along any distinct paths joining two vertices are the same or within some small error factor. We use PageRank vectors as well as tools related to the Cheeger constant to give a clustering algorithm that runs in nearly linear time.

4 A Cut-Based Analysis We next proceed to exploring networks where an adversarial infection can infect polynomially more nodes than the oblivious stochastic strategy. We will show that two important parameters in understanding this goal is the value of the max minimum weighted cut, Φmin G , and the value of maximum weighted cut, ΦG , in the input graph G. is at least logarithmically large the oblivious We ﬁrst show that if Φmin G stochastic strategy is essentially pandemic. Theorem 3 (Theorem 1 of [2]).