Community Search Problem Research Articles

Conditional Community Search Based on Weight Information

Community search aims to identify cohesive subgraphs containing user-given query nodes in social networks. As information technology develops, user demands for community search have become increasingly sophisticated. The searched communities must not only meet the structural cohesiveness requirements but also adhere to some complex search conditions based on Boolean expressions. For example, certain desired nodes should be contained in the communities, while certain undesired nodes cannot exist in the communities, which is called conditional community search. However, existing solutions for conditional community search often introduce some undesired nodes into the identified communities and exhibit relatively low search efficiency. To overcome these drawbacks, therefore, this paper investigates the problem of conditional community search based on weight information. First, we refine the original problem definition of conditional community search and outline the need for an improved algorithm for calculating the weights of the nodes. Then, we explore two novel algorithms for searching conditional communities based on calculated weight information. Finally, we conduct extensive experiments on several real-world datasets to verify the accuracy and efficiency of our proposed searching algorithms.

CCSS: Towards conductance-based community search with size constraints

Size-constrained community search, retrieving a size-bounded high-quality subgraph containing user-specified query vertices, has been extensively studied in graph analysis. However, existing methods mainly focus on the cohesiveness within the community while ignoring its separation from the outside, leading to sub-optimal results. Inspired by this, we adopt the well-known conductance to measure the quality of a community and introduce a novel problem of Conductance-based Community Search with Size Constraints (CCSS). CCSS aims to identify a subgraph with the smallest conductance among all connected subgraphs that contain the query vertex q and have at least l and at most h vertices. We prove that CCSS is NP-hard. To efficiently address CCSS, we first propose a computational framework ISC with two-level loops. In the inner loop, ISC starts from q and iteratively adds vertices based on the predefined score function, obtaining a coarse-grained candidate community. In the outer loop, we design the perturbation strategy to repeatedly execute the inner loop until the quality of the candidate community converges. Then, we propose two heuristic algorithms, ISCCI and ISCCP, to concretely implement the score function and perturbation strategy of ISC, which significantly reduce the computational costs. Finally, empirical results demonstrate the superiorities of our solutions. Our source codes and datasets are available at https://github.com/longlonglin/CCSS.

Efficient Community Search in Edge-Attributed Graphs

Given a graph, searching for a community containing a query vertex is a fundamental problem and has found many applications. Most existing community search models are based on non-attributed or vertex-attributed graphs. In many real-world graphs, however, the edges carry the richest information to describe the interactions between vertices; hence, it is important to take the information into account in community search. In this paper, we conduct a pioneer study on the community search on edge-attributed graphs. We proposed the Edge-Attributed Community Search (EACS) problem, which aims to extract a subgraph that contains the given query vertex while its edges have the maximum attribute similarity. We prove that the EACS problem is NP-hard and propose both exact and 2-approximation algorithms to address EACS. Our exact algorithms run up to 2320.34 times faster than the baseline solution. Our approximate algorithms further improve the efficiency by up to 2.93 times. We conducted extensive experiments to demonstrate the efficiency and effectiveness of our algorithms.

Attribute-sensitive community search over attributed heterogeneous information networks

Community search (CS) over attributed heterogeneous information networks (AHINs) takes both network structure and attributes of nodes into consideration, which can support personalized requirement and has gained great interest recently. Nevertheless, existing works are insensitive to the attributes that results from two limitations: (1) The structural cohesiveness metrics is insensitive to the slight quantity changes of nodes in a community. (2) The measurement adopted to measure the relevance between a community and given keywords is inappropriate. Additionally, the insensitivity may also lead to the free rider effect. To deal with these issues, in this paper, we first define structural cohesiveness by using the minimum number of neighbor nodes connected to each node in the community through a meta-path, then define keyword density with the path instances containing the given keywords, afterwards integrate both of them to propose an attribute-sensitive community model ASC that is sensitive to the attributes, and present the CS problem. In order to search community, we first propose a basic CS algorithm, then develop two index based CS algorithms to improve the efficiency, and theoretically prove that these two index based algorithms are more efficient than the basic algorithm. Comprehensive experiments conducted on five real-world datasets demonstrate the effectiveness of ASC and the efficiency of the developed algorithms.

Influential Community Search over Large Heterogeneous Information Networks

Recently, the topic of influential community search has gained much attention. Given a graph, it aims to find communities of vertices with high importance values from it. Existing works mainly focus on conventional homogeneous networks, where vertices are of the same type. Thus, they cannot be applied to heterogeneous information networks (HINs) like bibliographic networks and knowledge graphs, where vertices are of multiple types and their importance values are of heterogeneity (i.e., for vertices of different types, their importance meanings are also different). In this paper, we study the problem of influential community search over large HINs. We introduce a novel community model, called heterogeneous influential community (HIC), or a set of closely connected vertices that are of the same type and high importance values, using the meta-path-based core model. An HIC not only captures the importance of vertices in a community, but also considers the influence on meta-paths connecting them. To search the HICs, we mainly consider meta-paths with two and three vertex types. Then, we develop basic algorithms by iteratively peeling vertices with low importance values, and further propose advanced algorithms by identifying the key vertices and designing pruning strategies that allow us to quickly eliminate vertices with low importance values. Extensive experiments on four real large HINs show that our solutions are effective for searching HICs, and the advanced algorithms significantly outperform baselines.

Efficient Influential Community Search in Large Uncertain Graphs

Influential community search aims to find cohesive subgraphs (communities) with considerable influence. It is a fundamental graph management operator that can play a crucial role in biological network analysis, activity organization, and other real-life applications. Existing research on influential community search is mainly focused on deterministic graphs with the assumption that influences between entities are certain. This assumption is invalid in many cases because it ignores the uncertainty which is an inherent property of influence. Against this backdrop, in this paper, we introduce an uncertain influential community model, namely <inline-formula><tex-math notation="LaTeX">$(k, \eta)$</tex-math></inline-formula> -influential community, based on which the influential community search problem over uncertain graphs is formulated. Furthermore, we propose an online approach by integrating a peeling-pruning strategy that can progressively refine the given uncertain graph to find the <inline-formula><tex-math notation="LaTeX">$(k, \eta)$</tex-math></inline-formula> -influential communities. To further improve the search performance, two novel indexes, ICU-Index and FICU-Index, are developed to organize the <inline-formula><tex-math notation="LaTeX">$(k, \eta)$</tex-math></inline-formula> -influential communities at different probabilistic intervals. The indexes decompose the probabilistic interval into multiple subintervals and based on this, the <inline-formula><tex-math notation="LaTeX">$(k, \eta)$</tex-math></inline-formula> -influential communities are divided into different groups in turn. Compared with ICU-Index, FICU-Index requires considerably less space with the introduction of two optimization strategies. These indexes help obtain results of an influential community search problem more efficiently. Extensive experiments on large real and synthetic datasets demonstrate the efficiency and effectiveness of our proposed algorithms.

Effective Community Search on Large Attributed Bipartite Graphs

Community search over bipartite graphs has attracted significant interest recently. In many applications such as the user–item bipartite graph in e-commerce and customer–movie bipartite graph in movie rating website, nodes tend to have attributes. However, the previous community search algorithms on bipartite graphs ignore attributes, thus making them to return results with poor cohesion with respect to their node attributes. In this paper, we study the community search problem on attributed bipartite graphs. Given a query vertex [Formula: see text], we aim to find the attributed [Formula: see text]-communities of [Formula: see text], where the structure cohesiveness of the community is described by the [Formula: see text]-core model, and the attribute similarity of two groups of nodes in the subgraph is maximized. In order to retrieve attributed communities from bipartite graphs, we first propose a basic algorithm composed of two steps: the generation and verification of candidate keyword sets, and then two improved query algorithms Inc and Dec are proposed. Inc is proposed considering the anti-monotonicity property of attributed bipartite graphs, then we adopt different generating methods and verify the order of candidate keyword sets and propose the Dec algorithm. After evaluating our solutions on eight large graphs, the experimental results demonstrate that our methods are effective and efficient in querying the attributed communities on bipartite graphs.

FirmTruss Community Search in Multilayer Networks

In applications such as biological, social, and transportation networks, interactions between objects span multiple aspects. For accurately modeling such applications, multilayer networks have been proposed. Community search allows for personalized community discovery and has a wide range of applications in large real-world networks. While community search has been widely explored for single-layer graphs, the problem for multilayer graphs has just recently attracted attention. Existing community models in multilayer graphs have several limitations, including disconnectivity, free-rider effect, resolution limits, and inefficiency. To address these limitations, we study the problem of community search over large multilayer graphs. We first introduce FirmTruss , a novel dense structure in multilayer networks, which extends the notion of truss to multilayer graphs. We show that FirmTrusses possess nice structural and computational properties and bring many advantages compared to the existing models. Building on this, we present a new community model based on FirmTruss, called FTCS , and show that finding an FTCS community is NP-hard. We propose two efficient 2-approximation algorithms, and show that no polynomial-time algorithm can have a better approximation guarantee unless P = NP. We propose an index-based method to further improve the efficiency of the algorithms. We then consider attributed multilayer networks and propose a new community model based on network homophily. We show that community search in attributed multilayer graphs is NP-hard and present an effective and efficient approximation algorithm. Experimental studies on real-world graphs with ground-truth communities validate the quality of the solutions we obtain and the efficiency of the proposed algorithms.

Effective community search over large star-schema heterogeneous information networks

Community search (CS) enables personalized community discovery and has found a wide spectrum of emerging applications such as setting up social events and friend recommendation. While CS has been extensively studied for conventional homogeneous networks, the problem for heterogeneous information networks (HINs) has received attention only recently. However, existing studies suffer from several limitations, e.g., they either require users to specify a meta-path or relational constraints, which pose great challenges to users who are not familiar with HINs. To address these limitations, in this paper, we systematically study the problem of CS over large star-schema HINs without asking users to specify these constraints; that is, given a set Q of query vertices with the same type, find the most-likely community from a star-schema HIN containing Q , in which all the vertices are with the same type and close relationships. To capture the close relationships among vertices of the community, we employ the meta-path-based core model, and maximize the number of shared meta-paths such that each of them results in a cohesive core containing Q. To enable efficient CS, we first develop online algorithms via exploiting the anti-monotonicity property of shared meta-paths. We further boost the efficiency by proposing a novel index and an efficient index-based algorithm with elegant pruning techniques. Extensive experiments on four real large star-schema HINs show that our solutions are effective and efficient for searching communities, and the index-based algorithm is much faster than the online algorithms.

Butterfly-core community search over labeled graphs

Community search aims at finding densely connected subgraphs for query vertices in a graph. While this task has been studied widely in the literature, most of the existing works only focus on finding homogeneous communities rather than heterogeneous communities with different labels. In this paper, we motivate a new problem of cross-group community search, namely Butterfly-Core Community (BCC), over a labeled graph, where each vertex has a label indicating its properties and an edge between two vertices indicates their cross relationship. Specifically, for two query vertices with different labels, we aim to find a densely connected cross community that contains two query vertices and consists of butterfly networks, where each wing of the butterflies is induced by a k-core search based on one query vertex and two wings are connected by these butterflies. We first develop a heuristic algorithm achieving 2-approximation to the optimal solution. Furthermore, we design fast techniques of query distance computations, leader pair identifications, and index-based BCC local explorations. Extensive experiments on seven real datasets and four useful case studies validate the effectiveness and efficiency of our BCC and its multi-labeled extension models.

I/O efficient k-truss community search in massive graphs

Community detection that discovers all densely connected communities in a network has been studied a lot. In this paper, we study online community search for query-dependent communities, which is a different but practically useful task. 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 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. We also investigate the k-truss community search problem in a dynamic graph setting with frequent insertions and deletions of graph vertices and edges. In addition, to support k-truss community search over massive graphs which cannot entirely fit in main memory, we propose I/O-efficient algorithms for query processing under the semi-external model. Extensive experiments on massive real-world networks demonstrate the effectiveness of our k-truss community model, the efficiency, and the scalability of our in-memory and semi-external community search algorithms.

An Approach of Community Search with Minimum Spanning Tree Based on Node Embedding

Community search is a query-oriented variant of community detection problem, and the goal is to retrieve a single community from a given set of nodes. Most of the existing community search methods adopt handcrafted features, so there are some limitations in applications. Our idea is motivated by the recent advances of node embedding. Node embedding uses deep learning method to obtain feature representation of nodes directly from graph structure automatically and offers a new method to measure the distance between two nodes. In this paper, we propose a two-stage community search algorithm with a minimum spanning tree strategy based on node embedding. At the first stage, we propose a node embedding model NEBRW and map nodes to the points in a low-dimensional vector space. At the second stage, we propose a new definition of community from the distance viewpoint, transform the problem of community search to a variant of minimum spanning tree problem, and uncover the target community with an improved Prim algorithm. We test our algorithm on both synthetic and real-world network datasets. The experimental results show that our algorithm is more effective for community search than baselines.

Efficient size-bounded community search over large networks

The problem of community search, which aims to find a cohesive subgraph containing user-given query vertices, has been extensively studied recently. Most of the existing studies mainly focus on the cohesiveness of the returned community, while ignoring the size of the community, and may yield communities of very large sizes. However, many applications naturally require that the number of vertices/members in a community should fall within a certain range. In this paper, we design exact algorithms for the general size-bounded community search problem that aims to find a subgraph with the largest min-degree among all connected subgraphs that contain the query vertex q and have at least l and at most h vertices, where q, l, h are specified by the query. As the problem is NP-hard, we propose a branch-reduce-and-bound algorithm SC-BRB by developing nontrivial reducing techniques, upper bounding techniques, and branching techniques. Experiments on large real graphs show that SC-BRB on average increases the minimum degree of the community returned by the state-of-the-art heuristic algorithm GreedyF by a factor of 2.41 and increases the edge density by a factor of 2.2. In addition, SC-BRB is several orders of magnitude faster than a baseline approach, and all of our proposed techniques contribute to the efficiency of SC-BRB.

Attributed community search based on effective scoring function and elastic greedy method

In recent years, with the proliferation of rich attribute information available for entities in real-world networks and the increasing demand for more personalized community searches, attributed community search (ACS), an upgraded version of the community search problem, has attracted great attention from the both academic and industry areas. Some algorithms have been proposed to solve this novel research problem. However, they have a deficiency in evaluating the quality of the attributed community structure, which may mislead them and discover less valuable structures. In this paper, we make up for this defect, and propose the SFEG algorithm to better solve the ACS problem. SFEG designs a more effective scoring function to measure the quality of the discovered attributed community structure, and presents an elastic greedy optimization method to quickly maximize the function value to determine the target community with a specific meaning. The extensive experiments conducted on the attributed graph datasets with ground-truth communities show that our algorithm significantly outperforms the state-of-the-art.

Discovering Significant Communities on Bipartite Graphs: An Index-based Approach

Bipartite graphs are widely used to model relationships between two types of entities. Community search retrieves densely connected subgraphs containing a query vertex, which has been extensively studied on unipartite graphs. However, it remains largely unexplored on bipartite graphs. Moreover, all existing cohesive subgraph models on bipartite graphs only measure the structure cohesiveness while overlooking the edge weight. In this paper, we study the significant (alpha, beta)-community search problem on weighted bipartite graphs. Given a query vertex q, we aim to find the significant (alpha, beta)-community R of q which adopts (alpha, beta)-core to characterize the engagement level of vertices, and maximizes the minimum edge weight (significance) within R. To support fast retrieval of R, we first obtain the maximal connected subgraph of (alpha, beta)-core containing q (the (alpha, beta)-community), and the search space is limited to this subgraph with a much smaller size than the original graph. A novel index structure is presented to support retrieving the (alpha, beta)-community in optimal time. Efficient index maintenance techniques are also proposed to handle dynamic graphs. To further obtain R, we develop peeling and expansion algorithms. The experimental results on real graphs validate the effectiveness and efficiency of our proposed techniques.

Influential Attributed Communities Search in Large Networks (InfACom)

Community search is a fundamental problem in graph analysis. In many applications, network nodes have specific properties that are essential for making sense of communities. In these networks, attributes are associated with nodes to capture their properties. The community influence is a key property of the community that can be employed to sort the communities in a network based on the relevance/importance of certain attributes. Unfortunately, most of the previously introduced community search algorithms over attributed networks neglected the community influence. In this paper, we study the influential attributed community search problem. Different factors for measuring the influence are discussed. Also, different Influential Attributed Community (InfACom) algorithms based on the concept of k-clique are proposed. Two techniques are presented one for sequential implementation with three variations and one for parallel implementation. In addition, we propose efficient algorithms for maintaining the proposed algorithms on dynamic graphs. The proposed algorithms are evaluated on different real datasets. The experimental results show that the summarization technique reduces the size of the graph by approximately half. In addition, it shows that the proposed algorithms $EnhancedExact$ and $Approximate$ outperform the state-of-the-art approaches Incremental Time efficient $(Inc-T)$ , Incremental Space efficient $(Inc-S)$ , $Exact$ , and 2-Approximation $(AppInc)$ in both efficiency and effectiveness. For the $EnhancedExact$ algorithm, the results show that the efficiency is at least 7 times faster than the $Inc-S$ algorithm, at least 4.5 times faster than the $Inc-T$ algorithm, and 2 times faster than the $AppInc$ algorithm. For the $Approximate$ algorithm, the results show that its efficiency is at least 10 times faster than the $Inc-S$ algorithm, at least 6.4 times faster than the $Inc-T$ algorithm, and 3 times faster than the $AppInc$ algorithm. Finally, the results show that the proposed algorithms retrieve cohesive communities with a smaller diameter than all the state-of-the-art approaches.

Topic-based community search over spatial-social networks

Recently, the community search problem has attracted significant attention, due to its wide spectrum of real-world applications such as event organization, friend recommendation, advertisement in e-commence, and so on. Given a query vertex, the community search problem finds dense subgraph that contains the query vertex. In social networks, users have multiple check-in locations, influence score, and profile information (keywords). Most previous studies that solve the CS problem over social networks usually neglect such information in a community. In this paper, we propose a novel problem, named community search over spatial-social networks (TCS-SSN), which retrieves community with high social influence, small traveling time, and covering certain keywords. In order to tackle the TCS-SSN problem over the spatial-social networks, we design effective pruning techniques to reduce the problem search space. We also propose an effective indexing mechanism, namely social-spatial index, to facilitate the community query, and develop an efficient query answering algorithm via index traversal. We verify the efficiency and effectiveness of our pruning techniques, indexing mechanism, and query processing algorithm through extensive experiments on real-world and synthetic data sets under various parameter settings.

Effective and efficient community search over large heterogeneous information networks

Recently, the topic of community search (CS) has gained plenty of attention. Given a query vertex, CS looks for a dense subgraph that contains it. Existing studies mainly focus on homogeneous graphs in which vertices are of the same type, and cannot be directly applied to heterogeneous information networks (HINs) that consist of multi-typed, interconnected objects, such as the bibliographic networks and knowledge graphs. In this paper, we study the problem of community search over large HINs; that is, given a query vertex q , find a community from an HIN containing q , in which all the vertices are with the same type of q and have close relationships. To model the relationship between two vertices of the same type, we adopt the well-known concept of meta-path , which is a sequence of relations defined between different types of vertices. We then measure the cohesiveness of the community by extending the classic minimum degree metric with a meta-path. We further propose efficient query algorithms for finding communities using these cohesiveness metrics. We have performed extensive experiments on five real large HINs, and the results show that the proposed solutions are effective for searching communities. Moreover, they are much faster than the baseline solutions.

Community search for multiple nodes on attribute graphs

Community search is individualized and targeted, which identifies local communities containing query nodes and meeting specific conditions only according to users. Community search is only interested in communities that satisfy the designated criteria, and has a wide range of application scenarios in the real world. Traditional community search only uses the topology information, without considering the impact of node attributes information. And many existing algorithms can only deal with a single query node. Therefore, this paper defines the attribute community search problem of multiple query nodes on attribute graphs, which utilizes the edge connectivity as the structural tightness constraint and designs an attribute function as the attribute tightness constraint. To solve this problem, we design a framework that firstly finds the maximum k edge connected-component containing query as a candidate subgraph, then iteratively deletes the node with the least contribution to the attribute function from the candidate subgraph and adjusts the subgraph according to the structural constraints. We also design the attribute Steiner distance that synthesizes the structural information and attribute information, and propose an efficient heuristic expansion algorithm based on distance. The experimental results on several datasets show our proposed methods can find the community containing all query nodes with high tightness of structure and homogeneity of attributes.

Effective and Efficient Community Search Over Large Directed Graphs

Communities are prevalent in social networks, knowledge graphs, and biological networks. Recently, the topic of community search (CS), extracting a dense subgraph containing a query vertex $q$q from a graph, has received great attention. However, existing CS solutions are designed for undirected graphs, and overlook directions of edges which potentially lose useful information carried on directions. In many applications (e.g., Twitter), users’ relationships are often modeled as directed graphs (e.g., if a user $a$a follows another user $b$b, then there is an edge from $a$a to $b$b). In this paper, we study the problem of CS on directed graph. Given a vertex $q$q of a graph $G$G, we aim to find a densely connected subgraph containing $q$q from $G$G, in which vertices have strong interactions and high similarities, by using the minimum in/out-degrees metric. We first develop a baseline algorithm based on the concept of D-core. We further propose three index structures and corresponding query algorithms. Our experimental results on seven real graphs show that our solutions are very effective and efficient. For example, on a graph with over 1 billion of edges, we only need around 40mins to index it and 1$\sim$∼2sec to answer a query.