By Anthony Bonato, Fan Chung Graham, Pawel Pralat

ISBN-10: 3319131222

ISBN-13: 9783319131221

ISBN-10: 3319131230

ISBN-13: 9783319131238

This publication constitutes the refereed court cases of the eleventh overseas Workshop on Algorithms and types for the net Graph, WAW 2014, held in Beijing, China, in December 2014.

The 12 papers awarded have been conscientiously reviewed and chosen for inclusion during this quantity. the purpose of the workshop was once to extra the certainty of graphs that come up from the net and diverse consumer actions on the net, and stimulate the improvement of high-performance algorithms and purposes that take advantage of those graphs. The workshop accumulated the researchers who're engaged on graph-theoretic and algorithmic elements of similar advanced networks, together with social networks, quotation networks, organic networks, molecular networks, and different networks coming up from the Internet.

**Read or Download Algorithms and Models for the Web Graph: 11th International Workshop, WAW 2014, Beijing, China, December 17-18, 2014, Proceedings PDF**

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**Extra resources for Algorithms and Models for the Web Graph: 11th International Workshop, WAW 2014, Beijing, China, December 17-18, 2014, Proceedings**

**Sample text**

In this paper we prove that if the degree distribution obeys the power law with an inﬁnite variance, then the global clustering coeﬃcient tends to zero with high probability as the size of a graph grows. 1 Introduction In this paper, we analyze the global clustering coeﬃcient of graphs with a powerlaw degree distribution. Namely, we consider a sequence of graphs with the degree distribution following a regularly varying distribution F . Our main result is the following. If the degree distribution has an inﬁnite variance, then the global clustering coeﬃcient tends to zero with high probability.

The ﬁrst deﬁnition of clustering coeﬃcient that we consider has been introduced by Onnela et al. [21]: W CvOnnela = u,w ∈W (v,G) w(e(v, ˆ u))w(e(v, ˆ w))w(e(u, ˆ w)) |N (v, G)| (|N (v, G)| − 1) . where with w(e(v, u)) we indicate the weight of the edge e(v, u) and w(e(·, ˆ ·)) = w(e(·,·)) . W Barrat et al. The second deﬁnition of clustering coeﬃcient that we consider has been introduced by Barrat et al. [2]: W CvBarrat = u,w ∈W (v,G) (w(e(v, u)) (|N (v, G)| − 1) + w(e(v, w)))1e(u,w) v∈e w(e) . where 1e(u,w) is equal 1 if the edge (u, w) exists and 0 otherwise.

The Location-of-Restart Personalized PageRank admits an even more elegant relation between the “direct” and “reverse” PageRanks in the case of undirected graphs: Theorem 4 (Symmetry for undirected Location-of-Restart Personalized PageRank). When W T = W and αi ∈ (0, 1), the following relation holds 1 − αi 1 − αj dj ρi (j) = di ρj (i). (16) αj αi A probabilistic proof follows from (12) and (15). , αi and di ) have an eﬀect on the relation between the “direct” and “reverse” PageRanks. We have no intuitive explanation of this distinction.