Author(s): Alan Gabel, P. L. Krapivsky, and S. Redner
We introduce a class of networks that grow by enhanced redirection. Nodes are introduced sequentially, and each either attaches to a randomly chosen target node with probability 1−r or to the parent of the target with probability r, where r is an increasing function of the degree of the parent. This...
[Phys. Rev. E 88, 050802] Published Tue Nov 12, 2013
Stochastic blockmodels are generative network models where the vertices are separated into discrete groups, and the probability of an edge existing between two vertices is determined solely by their group membership. In this paper, we derive expressions for the entropy of stochastic blockmodel ensembles. We consider several ensemble variants, including the traditional model as well as the newly introduced degree-corrected version [Karrer et al. Phys. Rev. E 83, 016107 (2011)], which imposes a degree sequence on the vertices, in addition to the block structure. The imposed degree sequence is implemented both as "soft" constraints, where only the expected degrees are imposed, and as "hard" constraints, where they are required to be the same on all samples of the ensemble. We also consider generalizations to multigraphs and directed graphs. We illustrate one of many applications of this measure by directly deriving a log-likelihood function from the entropy expression, and using it to infer latent block structure in observed data. Due to the general nature of the ensembles considered, the method works well for ensembles with intrinsic degree correlations (i.e. with entropic origin) as well as extrinsic degree correlations, which go beyond the block structure.
Author(s): Yanqing Hu, Dong Zhou, Rui Zhang, Zhangang Han, Céline Rozenblat, and Shlomo Havlin
Real data show that interdependent networks usually involve intersimilarity. Intersimilarity means that a pair of interdependent nodes have neighbors in both networks that are also interdependent [ Parshani et al. Europhys. Lett. 92 68002 (2010)]. For example, the coupled worldwide port network and...
[Phys. Rev. E 88, 052805] Published Thu Nov 07, 2013
Author(s): Adilson E. Motter, Márton Gruiz, György Károlyi, and Tamás Tél
Chaos is an inherently dynamical phenomenon traditionally studied for trajectories that are either permanently erratic or transiently influenced by permanently erratic ones lying on a set of measure zero. The latter gives rise to the final state sensitivity observed in connection with fractal basin ...
[Phys. Rev. Lett. 111, 194101] Published Thu Nov 07, 2013