Community detection which discovers densely connected structures in a network has been studied a lot. In this paper, we study online community search which is practically useful but less studied in the literature. Given a query vertex in a graph, the problem is to find meaningful communities that the vertex belongs to in an online manner. We propose a novel community model based on the k-truss concept, which brings nice structural and computational properties. We design a compact and elegant index structure which supports the efficient search of k-truss communities with a linear cost with respect to the community size. In addition, we investigate the ktruss community search problem in a dynamic graph setting with frequent insertions and deletions of graph vertices and edges. Extensive experiments on large real-world networks demonstrate the effectiveness and efficiency of our community model and search algorithms.

Recently, there has been significant interest in the study of the community search problem in social and information networks: given one or more query nodes, find densely connected communities containing the query nodes. However, most existing studies do not address the "free rider" issue, that is, nodes far away from query nodes and irrelevant to them are included in the detected community. Some state-of-the-art models have attempted to address this issue, but not only are their formulated problems NP-hard, they do not admit any approximations without restrictive assumptions, which may not always hold in practice.In this paper, given an undirected graph G and a set of query nodes Q, we study community search using the k-truss based community model. We formulate our problem of finding a closest truss community (CTC), as finding a connected k-truss subgraph with the largest k that contains Q, and has the minimum diameter among such subgraphs. We prove this problem is NP-hard. Furthermore, it is NP-hard to approximate the problem within a factor (2−ε), for any ε > 0. However, we develop a greedy algorithmic framework, which first finds a CTC containing Q, and then iteratively removes the furthest nodes from Q, from the graph. The method achieves 2-approximation to the optimal solution. To further improve the efficiency, we make use of a compact truss index and develop efficient algorithms for k-truss identification and maintenance as nodes get eliminated. In addition, using bulk deletion optimization and local exploration strategies, we propose two more efficient algorithms. One of them trades some approximation quality for efficiency while the other is a very efficient heuristic. Extensive experiments on 6 real-world networks show the effectiveness and efficiency of our community model and search algorithms.

Recently, community search over graphs has attracted significant attention and many algorithms have been developed for finding dense subgraphs from large graphs that contain given query nodes. In applications such as analysis of protein protein interaction (PPI) networks, citation graphs, and collaboration networks, nodes tend to have attributes. Unfortunately, most previously developed community search algorithms ignore these attributes and result in communities with poor cohesion w.r.t. their node attributes. In this paper, we study the problem of attribute-driven community search, that is, given an undirected graph G where nodes are associated with attributes, and an input query Q consisting of nodes Vq and attributes Wq, find the communities containing Vq, in which most community members are densely inter-connected and have similar attributes.We formulate our problem of finding attributed truss communities (ATC), as finding all connected and close k-truss subgraphs containing Vq, that are locally maximal and have the largest attribute relevance score among such subgraphs. We design a novel attribute relevance score function and establish its desirable properties. The problem is shown to be NP-hard. However, we develop an efficient greedy algorithmic framework, which finds a maximal k-truss containing Vq, and then iteratively removes the nodes with the least popular attributes and shrinks the graph so as to satisfy community constraints. We also build an elegant index to maintain the known k-truss structure and attribute information, and propose efficient query processing algorithms. Extensive experiments on large real-world networks with ground-truth communities shows the efficiency and effectiveness of our proposed methods.

With the rapid development of information technologies, various big graphs are prevalent in many real applications (e.g., social media and knowledge bases). An important component of these graphs is the network community. Essentially, a community is a group of vertices which are densely connected internally. Community retrieval can be used in many real applications, such as event organization, friend recommendation, and so on. Consequently, how to efficiently find high-quality communities from big graphs is an important research topic in the era of big data. Recently a large group of research works, called community search, have been proposed. They aim to provide efficient solutions for searching high-quality communities from large networks in real-time. Nevertheless, these works focus on different types of graphs and formulate communities in different manners, and thus it is desirable to have a comprehensive review of these works.In this survey, we conduct a thorough review of existing community search works. Moreover, we analyze

Internet traffic has Zipf-like properties at multiple aggregation levels. These properties suggest the possibility of offloading most of the traffic from a complex controller (e.g., a software router) to a simple forwarder (e.g., a commodity switch), by letting the forwarder handle a very limited set of flows; the heavy hitters. As the volume of traffic from a set of flows is highly dynamic, maintaining a reliable set of heavy hitters over time is challenging. This is especially true when we face a volume limit in the non-offloaded traffic in combination with a constraint in the size of the heavy hitter set or its rate of change. We propose a set selection strategy that takes advantage of the properties of heavy hitters at different time scales. Based on real Internet traffic traces, we show that our strategy is able to offload most of the traffic while limiting the rate of change of the heavy hitter set, suggesting the feasibility of alternative router designs.

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Social contagion depicts a process of information (e.g., fads, opinions, news) diffusion in the online social networks. A recent study reports that in a social contagion process the probability of contagion is tightly controlled by the number of connected components in an individual's neighborhood. Such a number is termed structural diversity of an individual and it is shown to be a key predictor in the social contagion process. Based on this, a fundamental issue in a social network is to find top-k users with the highest structural diversities. In this paper, we, for the first time, study the top-k structural diversity search problem in a large network. Specifically, we develop an effective upper bound of structural diversity for pruning the search space. The upper bound can be incrementally refined in the search process. Based on such upper bound, we propose an efficient framework for top-k structural diversity search. To further speed up the structural diversity evaluation in the search process, several carefully devised heuristic search strategies are proposed. Extensive experimental studies are conducted in 13 real-world large networks, and the results demonstrate the efficiency and effectiveness of the proposed methods.

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