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 pc ≈ 10%, there is a dramatic decrease in the time, Tc, taken for the entire population to adopt the committed opinion. In particular, for complete graphs we show that when p < pc, Tc ∼ exp(α(p)N ), while for p > pc, Tc ∼ ln N . We conclude with simulation results for Erdős-Rényi random graphs and scale-free networks which show qualitatively similar behavior.

Overlap is one of the characteristics of social networks, in which a person may belong to more than one social group. For this reason, discovering overlapping structures is necessary for realistic social analysis. In this paper, we present a novel, general framework to detect and analyze both individual overlapping nodes and entire communities. In this framework, nodes exchange labels according to dynamic interaction rules. A specific implementation called Speakerlistener Label Propagation Algorithm (SLPA 1 ) demonstrates an excellent performance in identifying both overlapping nodes and overlapping communities with different degrees of diversity.

Abstract. Membership diversity is a characteristic aspect of social networks in which a person may belong to more than one social group. For this reason, discovering overlapping structures is necessary for realistic social analysis. In this paper, we present a fast algorithm 1 , called SLPA, for overlapping community detection in large-scale networks. SLPA spreads labels according to dynamic interaction rules. It can be applied to both unipartite and bipartite networks. It is also able to uncover overlapping nested hierarchy. The time complexity of SLPA scales linearly with the number of edges in the network. Experiments in both synthetic and real-world networks show that SLPA has an excellent performance in identifying both node and community level overlapping structures.

Routing in delay tolerant networks is a challenging problem due to the intermittent connectivity between nodes resulting in the frequent absence of end-to-end path for any source-destination pair at any given time. Recently, this problem has attracted a great deal of interest and several approaches have been proposed. Since Mobile Social Networks (MSNs) are increasingly popular type of Delay Tolerant Networks (DTNs), making accurate analysis of social network properties of these networks is essential for designing efficient routing protocols. In this paper, we introduce a new metric that detects the quality of friendships between nodes accurately. Utilizing this metric, we define the community of each node as the set of nodes having close friendship relations with this node either directly or indirectly. We also present Friendship-Based Routing in which periodically differentiated friendship relations are used in forwarding of messages. Extensive simulations on both real and synthetic traces show that the introduced algorithm is more efficient than the existing algorithms.

This paper reviews the state of the art in overlapping community detection algorithms, quality measures, and benchmarks. A thorough comparison of different algorithms (a total of fourteen) is provided. In addition to community level evaluation, we propose a framework for evaluating algorithms' ability to detect overlapping nodes, which helps to assess over-detection and underdetection. After considering community level detection performance measured by Normalized Mutual Information, the Omega index, and node level detection performance measured by Fscore, we reached the following conclusions. For low overlapping density networks, SLPA, OSLOM, Game and COPRA offer better performance than the other tested algorithms. For networks with high overlapping density and high overlapping diversity, both SLPA and Game provide relatively stable performance. However, test results also suggest that the detection in such networks is still not yet fully resolved. 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.