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

This ebook constitutes the refereed court cases of the tenth foreign Workshop on Algorithms and types for the net Graph, WAW 2013, held in Cambridge, MA, united states, in December 2013. The 17 papers awarded have been rigorously reviewed and chosen for inclusion during this quantity. They handle themes on the topic of graph-theoretic and algorithmic facets of similar advanced networks, together with quotation networks, social networks, organic networks, molecular networks and different networks coming up from the Internet.

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Extra info for Algorithms and Models for the Web Graph: 10th International Workshop, WAW 2013, Cambridge, MA, USA, December 14-15, 2013, Proceedings

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In this paper we only consider adversarial infections that obey the first-order constraints; unless stated explicitly otherwise, an adversary would be assumed to obey the first-order constraints. We will call the problem of finding a firstorder constrained adversarial infection that maximizes number of infections the adversarial infection problem 1 . An adversarial strategy will be called pandemic if it infects all nodes. Independent Cascades Diffusion Model. The Independent Cascades (IC) model of diffusion was formalized by Kempe et al.

For the second part, we estimate both the number of triangles and the number of open triangles in Gt thanks to two applications of Theorem 1. We choose to count the triangles from their youngest vertex and consider the functional which associates to a vertex x the number of triangles containing x and having x as youngest vertex. The light-tail of the outdegree distribution ensures that this functional satisfies the uniform moment condition. We can apply Theorem 1 and deduce that the number of triangles is always asymptotically proportional to the number of vertices, that is of order t.

WAW 2007. LNCS, vol. 4863, pp. 41–55. Springer, Heidelberg (2007) 14. : Spatial preferential attachment networks: Power laws and clustering coefficients. 3830 (2012) 15. : Geometric graph properties of the spatial preferred attachment model. Adv. Appl. Math. 50, 243–267 (2013) 16. : Degree sequences of geometric preferential attachment graphs. Adv. in Appl. Probab. 42, 319–330 (2010) 17. : Continuum percolation. Cambridge Tracts in Mathematics, vol. 119. Cambridge University Press, Cambridge (1996) 18.

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