Algorithms and Dynamical Models for Communities and by Vincent Traag

By Vincent Traag

A chronic challenge while discovering groups in huge advanced networks is the so-called answer restrict. This thesis addresses this factor meticulously, and introduces the real inspiration of resolution-limit-free. Remarkably, purely few tools own this fascinating estate, and this thesis places ahead one such strategy. in addition, it discusses easy methods to verify no matter if groups can take place by accident or no longer. One element that's usually missed during this box is handled right here: hyperlinks is usually unfavourable, as in conflict or clash. in addition to tips to contain this in group detection, it additionally examines the dynamics of such unfavourable hyperlinks, encouraged through a sociological idea referred to as social stability. This has interesting connections to the evolution of cooperation, suggesting that for cooperation to emerge, teams frequently cut 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 hyperlinks.

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

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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. For the configuration null model we can choose a similar optimal parameter value, in order to detect the planted partition as well as possible.

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. Hence, we will introduce a mixing parameter 0 ≤ μ ≤ 1 such that each node will have about (1 − μ)⇒k⊆ edges within its community, and about μ⇒k⊆ edges outside its community. Such a network can be easily constructed as follows. We pick a random node i and with probability μ we will link to a node outside of its community, and with probability 1 − μ we link to a node within its community.

20, 22]. Instead of considering all possible changes, we simply choose a random new community for a node. Similarly, a change can consist of merging two communities. Finally, a change can consist of splitting a community in two. All changes have a certain associated change in the objective function of H and the change is accepted with probability Pr(accept change) = 1 exp(−β H) if if H < 0, H ≥ 0. 35) The change for moving a node i from community c to community d is already provided in Eq. 33).

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