Algorithms and Dynamical Models for Communities and by Vincent Traag PDF

By Vincent Traag

ISBN-10: 3319063901

ISBN-13: 9783319063904

ISBN-10: 331906391X

ISBN-13: 9783319063911

A power challenge whilst discovering groups in huge advanced networks is the so-called solution restrict. This thesis addresses this factor meticulously, and introduces the real concept of resolution-limit-free. Remarkably, basically few tools own this fascinating estate, and this thesis places ahead one such procedure. additionally, it discusses how you can investigate no matter if groups can take place unintentionally or now not. One point that's frequently overlooked during this box is handled right here: hyperlinks is additionally unfavorable, as in warfare or clash. in addition to easy methods to contain this in group detection, it additionally examines the dynamics of such adverse hyperlinks, encouraged through 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 impression of buying and selling groups on overseas clash, and the way groups shape in a quotation community with optimistic and adverse links.

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The expected code length per symbol is then 4 This could be expressed in a different base as well. Since the base only changes the properties up to a multiplicative constant, we ignore this and simply take the natural logarithm. 26 2 Community Detection pi bi = − i pi log pi = H (X ). i The amazing thing is that this is also the optimal code length per symbol. In other words, we cannot represent the information in a shorter code per symbol than the entropy. This is known as the famous Shannon source-coding theorem [9].

The first to propose such test networks were [18], and remained the common benchmark for some time [10]. In general, test networks are constructed as follows. We wish to build a network of q communities of each n c nodes with average degree ⇒k⊆. The total number of nodes is then n = qn c and the total number of edges m = ⇒k⊆n/2. Furthermore, we would like to control the difficulty of detecting communities. The denser communities are, and the better separated from the rest of the network, the easier it is to detect such communities.

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. 016114. 3083 50. Wasserman S, Faust K (1994) Social network analysis. Cambridge University Press, Cambridge 51. Xu R, Wunsch D (2008) Clustering.

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Algorithms and Dynamical Models for Communities and Reputation in Social Networks by Vincent Traag

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