Efficient Maximum Relative Fair Clique Computation in Attributed Graphs

Yufeng Zhang, Shiyuan Liu, Yanping Wu, Lu Qin, Ying Zhang

Abstract: Cohesive subgraph mining is a fundamental problem in attributed graph analysis. However, the existing models on attributed graphs ignore the fairness of attributes. In this paper, we propose a novel model, called maximum relative fair clique, which integrates cohesiveness and fair resource allocation. Specifically, given an attributed graph G and a positive integer $$\delta $$ , a relative fair clique is a clique where the number of vertices with the most common attribute minus the number of vertices with the least amount of the common attribute should be no more than $$\delta $$ . We aim to find the maximum relative fair clique, which is the maximal one with the largest size. To solve this problem, we develop an algorithm, MRFCSearch, equipped with a novel heuristic algorithm and an efficient pruning technique. We evaluate the algorithm on four real-world graphs, demonstrating the performance of the proposed techniques.