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Community search is the problem of finding a good community for a given set of query vertices. One of the most studied formulations of community search asks for a connected subgraph that contains all query vertices and maximizes the minimum degree. All existing approaches to min-degree-based community search suffer from limitations concerning efficiency, as they need to visit (large part of) the whole input graph, as well as accuracy, as they output communities quite large and not really cohesive. Moreover, some existing methods lack generality: they handle only single-vertex queries, find communities that are not optimal in terms of minimum degree, and/or require input parameters. In this work we advance the state of the art on community search by proposing a novel method that overcomes all these limitations: it is in general more efficient and effective-one/two orders of magnitude on average, it can handle multiple query vertices, it yields optimal communities, and it is parameterfree. These properties are confirmed by an extensive experimental analysis performed on various real-world graphs.

Given a directed social graph and a set of past information cascades observed over the graph, we study the novel problem of detecting modules of the graph (communities of nodes), that also explain the cascades. Our key observation is that both information propagation and social ties formation in a social network can be explained according to the same latent factor, which ultimately guide a user behavior within the network. Based on this observation, we propose the Community-Cascade Network (CCN) model, a stochastic mixture membership generative model that can fit, at the same time, the social graph and the observed set of cascades. Our model produces overlapping communities and for each node, its level of authority and passive interest in each community it belongs.For learning the parameters of the CCN model, we devise a Generalized Expectation Maximization procedure. We then apply our model to real-world social networks and information cascades: the results witness the validity of the proposed CCN model, providing useful insights on its significance for analyzing social behavior.

Modeling how information propagates in social networks driven by peer influence, is a fundamental research question towards understanding the structure and dynamics of these complex networks, as well as developing viral marketing applications. Existing literature studies influence at the level of individuals, mostly ignoring the existence of a community structure in which multiple nodes may exhibit a common influence pattern.In this paper we introduce CSI, a model for analyzing information propagation and social influence at the granularity of communities. CSI builds over a novel propagation model that generalizes the classic Independent Cascade model to deal with groups of nodes (instead of single nodes) influence. Given a social network and a database of past information propagation, we propose a hierarchical approach to detect a set of communities and their reciprocal influence strength. CSI provides a higher level and more intuitive description of the influence dynamics, thus representing a powerful tool to summarize and investigate patterns of influence in large social networks. The evaluation on various datasets suggests the effectiveness of the proposed approach in modeling information propagation at the level of communities. It further enables to detect interesting patterns of influence, such as the communities that play a key role in the overall diffusion process, or that are likely to start information cascades.