By Vincent Traag
A chronic challenge while discovering groups in huge complicated networks is the so-called answer restrict. This thesis addresses this factor meticulously, and introduces the $64000 concept of resolution-limit-free. Remarkably, in simple terms few equipment own this fascinating estate, and this thesis places ahead one such technique. additionally, it discusses the best way to examine even if groups can ensue accidentally or no longer. One element that's frequently missed during this box is taken care of right here: hyperlinks is additionally unfavorable, as in warfare or clash. in addition to the best way to contain this in group detection, it additionally examines the dynamics of such unfavourable hyperlinks, encouraged by means of a sociological concept often called social stability. This has fascinating 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 influence of buying and selling groups on foreign clash, and the way groups shape in a quotation community with confident and adverse links.
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Additional resources for Algorithms and Dynamical Models for Communities and Reputation in Social Networks
0018209. 0431 46. 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, conditioning always decreases the entropy. Furthermore, if X is completely determined by Y then H (X | Y ) = 0, which makes sense since knowing Y we also know X . 27) H (X, Y ) = − xy and hence H (X, Y ) = H (Y, X ) = H (Y | X ) + H (X ), = H (X | Y ) + H (Y ). If X and Y are independent random variables then H (X | Y ) = H (X ), and so H (X, Y ) = H (X ) + H (Y ). Since H (X | Y ) ≥ 0, we have H (X, Y ) ≥ H (X ) and H (X, Y ) ≥ H (Y ), and so the joint entropy is always larger than the entropy of a single random variable.
So, the total expected code length is then L(σ ) = (1 − ρ)Hq + qc Hc . 28) c This is known as the map equation, and we try to minimize this expected code length. The derivation here is slightly different from the original , but is similar in spirit. Unlike the other models, we will not analyse this model in great detail, but it is included for the sake of completeness. 8 Alternative Clustering Methods As stated earlier, the approach of community detection is somewhat recent, and different approaches have been used before.
Algorithms and Dynamical Models for Communities and Reputation in Social Networks by Vincent Traag