k-Clique counting on large scale-graphs: a survey

Clique counting is a crucial task in graph mining, as the count of cliques provides different insights across various domains, social and biological network analysis, community detection, recommendation systems, and fraud detection. Counting cliques is algorithmically challenging due to combinatorial explosion, especially for large datasets and larger clique sizes. There are comprehensive surveys and reviews on algorithms for counting subgraphs and triangles (three-clique), but there is a notable lack of reviews addressing k-clique counting algorithms for k > 3. This paper addresses this gap by reviewing clique counting algorithms designed to overcome this challenge. Also, a systematic analysis and comparison of exact and approximation techniques are provided by highlighting their advantages, disadvantages, and suitability for different contexts. It also presents a taxonomy of clique counting methodologies, covering approximate and exact methods and parallelization strategies. The paper aims to enhance understanding of this specific domain and guide future research of k-clique counting in large-scale graphs.