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

ISBN-10: 3642180086

ISBN-13: 9783642180088

ISBN-10: 3642180094

ISBN-13: 9783642180095

This e-book constitutes the refereed court cases of the seventh foreign Workshop on Algorithms and versions 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 net and community Economics (WINE 2010).

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

**Read Online or Download Algorithms and Models for the Web-Graph: 7th International Workshop, WAW 2010, Stanford, CA, USA, December 13-14, 2010. Proceedings PDF**

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**Additional resources for Algorithms and Models for the Web-Graph: 7th International Workshop, WAW 2010, Stanford, CA, USA, December 13-14, 2010. Proceedings**

**Example text**

If an attribute w is not discovered by time n − 1, we set Γw = ∞ and note that P[Γw = ∞] = (1 − pw )n . From the independence of the random variables Iv,w , it follows that the discovery times {Γw : w ∈ W } are mutually independent. We now focus on describing the distribution of φt = α∈Wt qα . For t ≥ 0, we have t φt = d qα = α∈Wt t I(Γw =j) qw = qα = j=0 α∈Wj \Wj−1 j=0 w∈W I(Γw ≤t) qw . t+1 1 − (1 − qw )(1 − qw ) . E[φt ] = (15) w∈W (16) w∈W The concentration of φ0 will be crucial for the analysis of the supercritical regime.

E 70(5), 056131 (2004) 9. : Modularity and community structure in networks. PNAS 103, 8577–8582 (2006) 10. 0 user manual. Technical Report SAND2009-6265, Sandia National Laboratories (2009) 11. : Performance criteria for graph clustering and markov cluster experiments. Technical Report INS-R0012, Centre for Mathematics and Computer Science (2000) Component Evolution in General Random Intersection Graphs Milan Bradonji´c1 , Aric Hagberg2, Nicolas W. Hengartner3, and Allon G. edu Abstract. Random intersection graphs (RIGs) are an important random structure with algorithmic applications in social networks, epidemic networks, blog readership, and wireless sensor networks.

Consider the size of the giant component. From the representation (15) 46 M. Bradonji´c et al. for φt−1 , consider the previously introduced random variables Xt,w = n log(1/(1 − pw ))I(Γw ≤ t). Similarly to the proof of Theorem 1, it follows that under the conditions of the theorem there is a positive constant δ > 0 such that w Xt,w is concentrated within (1 ± δ) w E[Xt,w ] = (1 ± δ)c/n, with probability 1 − o(1). Hence, there exists p+ = c+ /n, for some constant c+ > c > 1, such that 1 − φt−1 ≤ 1 − (1 − p+ )t , which is equivalent to − log φt−1 ≤ t log(1 − p+ ) = tp+ + o(tp+ ) = tc+ /n + o(t/n).

### Algorithms and Models for the Web-Graph: 7th International Workshop, WAW 2010, Stanford, CA, USA, December 13-14, 2010. Proceedings by Andrei Broder (auth.), Ravi Kumar, Dandapani Sivakumar (eds.)

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