Social consensus through the influence of committed minorities

We show how the prevailing majority opinion in a population can be rapidly reversed by a small fraction p of randomly distributed committed agents who consistently proselytize the opposing opinion and are immune to influence. Specifically, we show that when the committed fraction grows beyond a critical value p_c \approx 10%, there is a dramatic decrease in the time, T_c, taken for the entire population to adopt the committed opinion. In particular, for complete graphs we show that when p < p_c, T_c \sim \exp(\alpha(p)N), while for p > p_c, T_c \sim \ln N. We conclude with simulation results for Erd\H{o}s-R\'enyi random graphs and scale-free networks which show qualitatively similar behavior.

See http://arxiv.org/abs/1102.3931

Overlapping Community Detection in Networks: the State of the Art and Comparative Study

This paper reviews the state of the art in overlapping community detection algorithms, quality measures, and benchmarks. A thorough comparison of different algorithms is provided. In addition to community level evaluation, we propose a novel framework for evaluating algorithms' ability to detect overlapping nodes, which helps to assess overdetection and underdetection. We conclude that SLPA, OSLOM, Game, and COPRA offer the best performance. A common feature observed by various algorithms in real-world networks is the relatively small fraction of overlapping nodes (typically less than 30%), each of which belongs to only 2 or 3 communities.

See http://arxiv.org/abs/1110.5813