Finding $(\alpha, \beta, k)$-community on birpartite graph

Community search over bipartite graphs is a critical issue that has garnered considerable interest. Nevertheless, existing research often neglects the importance of vertex weights in community formation, which leads to the omission of valuable characteristics of the community. In this paper, we propose a new cohesive subgraph model named <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(\alpha,\beta,\ k)$</tex> -community that considers the average weight of vertices from two layers on bipartite graphs and limits the size <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k$</tex> of the graphs, thereby providing a more comprehensive reflection of community influence. Based on this community model, we propose both exact and approximate algorithms to find the community. Extensive experiments on 4 real-world graphs validate both the effectiveness and the efficiency of our algorithms.