Clique is one of the most fundamental models for cohesive subgraph mining in network analysis. Existing clique model mainly focuses on unsigned networks. In real world, however, many applications are modeled as signed networks with positive and negative edges. As the signed networks hold their own properties different from the unsigned networks, the existing clique model is inapplicable for the signed networks. Motivated by this, we propose the balanced clique model that considers the most fundamental and dominant theory, structural balance theory, for signed networks, and study the maximal balanced clique enumeration problem which computes all the maximal balanced cliques in a given signed network. We show that the maximal balanced clique enumeration problem is NP-Hard. A straightforward solution for the maximal balanced clique enumeration problem is to treat the signed network as two unsigned networks and leverage the off-the-shelf techniques for unsigned networks. However, such a solution is inefficient for large signed networks. To address this problem, in this paper, we first propose a new maximal balanced clique enumeration algorithm by exploiting the unique properties of signed networks. Based on the new proposed algorithm, we devise two optimization strategies to further improve the efficiency of the enumeration. We conduct extensive experiments on large real and synthetic datasets. The experimental results demonstrate the efficiency, effectiveness and scalability of our proposed algorithms.
With the prevalence of Internet access and online services, various big graphs are generated in many real applications (e.g., online social networks and knowledge graphs). An important task on analyzing and mining these graphs is keyword search. Essentially, given a graph G and query Q associated with a set of keywords, the keyword search aims to find a substructure (e.g., rooted tree or subgraph) S in G such that nodes in S collectively cover part of or all keywords in Q, and in the meanwhile, S is optimal on some user specified semantics. Keyword search on graphs can be applied in many real-life applications, such as point-of-interests recommendation and web search facility. In spite of the great importance of graph keyword search, we, however, notice that the latest survey on this topic is far out of date. Consequently, there is prompt need to conduct a comprehensive survey in this research direction. Motivated by this, in this survey, we systematically review graph keyword search studies by classifying the existing works into different categories according to the specific problem definition. This survey aims to provide the researchers a comprehensive understanding of existing graph keyword search solutions.
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