By Vincent Traag

A chronic challenge while discovering groups in huge complicated networks is the so-called solution restrict. This thesis addresses this factor meticulously, and introduces the $64000 suggestion of resolution-limit-free. Remarkably, in basic terms few equipment own this fascinating estate, and this thesis places ahead one such technique. furthermore, it discusses tips to check even if groups can take place by accident or no longer. One element that's usually neglected during this box is taken care of right here: hyperlinks can be detrimental, as in struggle or clash. along with find out how to contain this in neighborhood detection, it additionally examines the dynamics of such destructive hyperlinks, encouraged by way of a sociological idea referred to as social stability. This has exciting connections to the evolution of cooperation, suggesting that for cooperation to emerge, teams frequently break up in opposing factions. as well as those theoretical contributions, the thesis additionally comprises an empirical research of the impact of buying and selling groups on overseas clash, and the way groups shape in a quotation community with confident and detrimental hyperlinks.

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**Extra info for Algorithms and Dynamical Models for Communities and Reputation in Social Networks (Springer Theses)**

**Example text**

Schaeffer SE (2007) Graph clustering. Comput Sci Rev 1(1):27–64. 2007. 001 47. Theodoridis S, Koutroumbas K (2006) Pattern recognition. Academic Press, New York. ISBN 9780080513614 48. Tibély G, Kertész J (2008) On the equivalence of the label propagation method of community detection and a Potts model approach. Phys A Stat Mech Appl 387(19–20):4982–4984. doi:10. 024 49. Traag VA, Van Dooren P, Nesterov Y (2011) Narrow scope for resolution-limit-free community detection. Phys Rev E 84(1):016114.

In other words, they use almost the same weights as RB, but then adapted for the added self-loops of strength γAFG . 13b) where δi j = δ(i, j) = 1 if i = j and zero otherwise. 2 Canonical Community Detection 19 pi j (γAFG ) = (ki + γAFG )(ki + γAFG ) . 15) ij which is simply Eq. 7) with self-loops added. The benefit of this method is that it leaves unchanged properties that depend on the eigenvectors or on the difference of the eigenvalues. e. In = diag(1, . . , 1). e. Av = λv), then also A v = Av + γAFG In v = (λ + γAFG )v so that v is an eigenvector of A and λ + γAFG an eigenvalue of A .

013 35. Newman M (2004) Fast algorithm for detecting community structure in networks. Phys Rev E 69(6). 066133 36. Newman M (2010) Networks: an introduction. Oxford University Press, Oxford. ISBN 0199206651 37. Newman M, Girvan M (2004) Finding and evaluating community structure in networks. Phys Rev E 69(2):026113. 026113 38. Newman MEJ (2006) Finding community structure in networks using the eigenvectors of matrices. Phys Rev E 74(3):036104+. 036104 39. Porter MA, Onnela JP, Mucha PJ (2009) Communities in networks.