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.

It is widely realized that the integration of database and information retrieval techniques will provide users with a wide range of high quality services. In this paper, we study processing an l-keyword query, p 1 , p 2 , · · · , p l , against a relational database which can be modeled as a weighted graph, G(V, E). Here V is a set of nodes (tuples) and E is a set of edges representing foreign key references between tuples. Let V i ⊆ V be a set of nodes that contain the keyword p i . We study finding top-k minimum cost connected trees that contain at least one node in every subset V i , and denote our problem as GST-k. When k = 1, it is known as a minimum cost group Steiner tree problem which is NPComplete. We observe that the number of keywords, l, is small, and propose a novel parameterized solution, with l as a parameter, to find the optimal GST-1, in time complexity O(3 l n + 2 l ((l + log n)n + m)), where n and m are the numbers of nodes and edges in graph G. Our solution can handle graphs with a large number of nodes. Our GST-1 solution can be easily extended to support GST-k, which outperforms the existing GST-k solutions over both weighted undirected/directed graphs. We conducted extensive experimental studies, and report our finding.

Community search is a problem of finding densely connected subgraphs that satisfy the query conditions in a network, which has attracted much attention in recent years. However, all the previous studies on community search do not consider the influence of a community. In this paper, we introduce a novel community model called k-influential community based on the concept of k-core, which can capture the influence of a community. Based on the new community model, we propose a linear-time online search algorithm to find the top-r k-influential communities in a network. To further speed up the influential community search algorithm, we devise a linear-space index structure which supports efficient search of the top-r k-influential communities in optimal time. We also propose an efficient algorithm to maintain the index when the network is frequently updated. We conduct extensive experiments on 7 real-world large networks, and the results demonstrate the efficiency and effectiveness of the proposed methods.

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Subgraph enumeration aims to find all the subgraphs of a large data graph that are isomorphic to a given pattern graph. As the subgraph isomorphism operation is computationally intensive, researchers have recently focused on solving this problem in distributed environments, such as MapReduce and Pregel. Among them, the state-of-the-art algorithm, Twin TwigJoin, is proven to be instance optimal based on a left-deep join framework. However, it is still not scalable to large graphs because of the constraints in the left-deep join framework and that each decomposed component (join unit) must be a star. In this paper, we propose SEED - a scalable sub-graph enumeration approach in the distributed environment. Compared to Twin TwigJoin, SEED returns optimal solution in a generalized join framework without the constraints in Twin TwigJoin. We use both star and clique as the join units, and design an effective distributed graph storage mechanism to support such an extension. We develop a comprehensive cost model, that estimates the number of matches of any given pattern graph by considering power-law degree distribution in the data graph. We then generalize the left-deep join framework and develop a dynamic-programming algorithm to compute an optimal bushy join plan. We also consider overlaps among the join units. Finally, we propose clique compression to further improve the algorithm by reducing the number of the intermediate results. Extensive performance studies are conducted on several real graphs, one containing billions of edges. The results demonstrate that our algorithm outperforms all other state-of-the-art algorithms by more than one order of magnitude.

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

Efficiently computing k-edge connected components in a large graph, G = (V, E), where V is the vertex set and E is the edge set, is a long standing research problem. It is not only fundamental in graph analysis but also crucial in graph search optimization algorithms. Consider existing techniques for computing k-edge connected components are quite time consuming and are unlikely to be scalable for large scale graphs, in this paper we firstly propose a novel graph decomposition paradigm to iteratively decompose a graph G for computing its k-edge connected components such that the number of drilling-down iterations h is bounded by the "depth" of the k-edge connected components nested together to form G, where h usually is a small integer in practice. Secondly, we devise a novel, efficient threshold-based graph decomposition algorithm, with time complexity O(l × |E|), to decompose a graph G at each iteration, where l usually is a small integer with l ≪ |V|. As a result, our algorithm for computing k-edge connected components significantly improves the time complexity of an existing state-of-the-art technique from O(|V| 2 |E| + |V| 3 log |V|) to O(h × l × |E|). Finally, we conduct extensive performance studies on large real and synthetic graphs. The performance studies demonstrate that our techniques significantly outperform the state-of-the-art solution by several orders of magnitude.

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