Game Theory

Algorithms and Dynamical Models for Communities and by Vincent Traag PDF

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 thought of resolution-limit-free. Remarkably, in basic terms few equipment own this fascinating estate, and this thesis places ahead one such procedure. additionally, it discusses how one can check even if groups can happen unintentionally or now not. One point that's usually overlooked during this box is handled right here: hyperlinks is additionally destructive, as in conflict or clash. along with how you can include this in group detection, it additionally examines the dynamics of such unfavorable hyperlinks, encouraged by way of a sociological idea often called social stability. This has fascinating 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 includes 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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The problem of community detection is NP-hard in general [6], so that there is no (known5 ) efficient (polynomial time) algorithm for optimizing the objective function. The algorithms presented will thus be heuristics, and usually involve some stochasticity. This implies that it will not necessarily always find exactly the same partition. In fact, modularity often seems to have many near optimal partitions, making it difficult to obtain the global optimum, and the other methods are expected to show a similar degeneracy [19].

Other well known measures for comparing partitions are the (adjusted) rand index and Jaccard index [15, 47, 51]. This is based on checking how many pairs of nodes are clustered in the same manner. 51) cd where n cd denotes the number of nodes that are in community c in partition C and in community d in partition D. 52) c where n C c refers to the number of nodes in community c in partition C. 53) 2 namely the fraction of pairs of nodes that are classified in the same manner (belonging both to the same community is both partitions are both to different communities in both partitions).

For Infomap there is no parameter present, so there is little to choose there. For CPM there is no such “natural” parameter, and one would have to look which γCPM works best (we will touch upon this issue in Sect. 1). However, given that we know how we generate the benchmark networks, we can calculate the ∗ for uncovering the planted partition. Since the CPM model optimal parameter γCPM and the RB model are equal for the ER null model when using γCPM = γRB p, this also corresponds to the optimal parameter for the RB model with the ER null model.

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