Download Algorithms and Dynamical Models for Communities and by Vincent Traag PDF

By Vincent Traag

A chronic challenge while discovering groups in huge advanced networks is the so-called solution restrict. This thesis addresses this factor meticulously, and introduces the $64000 concept of resolution-limit-free. Remarkably, simply few tools own this fascinating estate, and this thesis places ahead one such procedure. in addition, it discusses find out how to examine even if groups can take place by accident or now not. One point that's frequently neglected during this box is handled the following: hyperlinks is also adverse, as in warfare or clash. along with how one can comprise this in neighborhood detection, it additionally examines the dynamics of such unfavourable hyperlinks, encouraged through a sociological idea often called social stability. This has interesting connections to the evolution of cooperation, suggesting that for cooperation to emerge, teams usually 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 foreign clash, and the way groups shape in a quotation community with optimistic and detrimental links.

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671 27. Kolaczyk ED (2009) Statistical analysis of network data: methods and models. Springer, Berlin. ISBN 9780387881461 28. Lambiotte R, Delvenne JC, Barahona M (2008) Laplacian dynamics and multiscale modular structure in, networks, pp 1–29. 1770 29. Lancichinetti A, Fortunato S (2009) Community detection algorithms: a comparative analysis. Phys Rev E 80(5):056117. 056117 30. Lancichinetti A, Fortunato S, Radicchi F (2008) Benchmark graphs for testing community detection algorithms. Phys Rev E 78(4):46110.

35) The change for moving a node i from community c to community d is already provided in Eq. 33). 37) with ecd = i j Ai j δ(σi , c)δ(σ j , d) the number of edges between c and d and ⇒ecd ⊆ the expected number of such edges. A random split is unlikely to improve the partition, so some additional effort should be made to find a reasonably good candidate split, for example by using the eigenvector split (see Sect. 4), but we will not consider that here. For both implementations the general idea remains the same.

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 actual codes attaining this bound are known as Huffman codes. For our purposes here, we do not need this machinery, and we will not discuss it further.

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