Abstract
In social networking analysis, there exists a fundamental problem called maximal cliques enumeration(MCE), which has been extensively investigated in many fields, including social networks, biological science, etc. As a matter of fact, the formation principle of maximal cliques that can help us to speed up the detection of maximal cliques from social networks is often ignored by most existing research works. Aiming to exploit the formation of maximal cliques in social networks, this paper pioneers a creative research issue on the detection of bases of maximal cliques in social networks. We propose a formal concept analysis-based approach for detecting the bases of maximal cliques and detection theorem. It is believed that our work can provide a new research solution and direction for future topological structure analysis in various complex networking systems.
Highlights
BackgroundRecent years witnessed the booming development of graph data modeling and its widely used applications
In [23], Pei et al proposed a method based on a topology for attributes of a formal context to generate the formal concept lattice, and the topology for attributes was induced by a reflexive and transitive relation on the set of attributes; by defining an equivalent relation on the topology for attributes, it has been proved that the formal concept lattice and the quotient topology for attributes decided by the equivalent relation is isomorphic
To detect the largest maximal cliques from the above network, we firstly find the base of the largest maximal cliques and exploit their formation principle
Summary
Recent years witnessed the booming development of graph data modeling and its widely used applications. Many applications can be represented with graph data modeling, such as social networks, web networks, and protein interactive networks. Analyzing and mining the useful knowledge from graphs is significantly meaningful. Maximal cliques enumeration (MCE) is an important research issue in graphs. A clique refers to a complete sub-graph where any two vertices are connected to each other. A maximal clique is a clique such that there is no clique with more vertices. The detection of maximal cliques or MCE is mainly to identify all maximal cliques because these cliques or maximal cliques contain more valued knowledge and information. MCE is widely used in community detection, topological analysis of web networks, and so forth
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