An Algorithm for Finding Optimal k-Core in Attribute Networks

As a structural indicator of dense subgraphs, k-core has been widely used in community search due to its concise and efficient calculation. Many community search algorithms have been expanded on the basis of k-core. However, relevant algorithms often set k values based on empirical analysis of datasets or require users to input manually. Once users are not familiar with the graph network structure, they may miss the optimal solution due to an improper k setting. Especially in attribute social networks, characterizing communities with only k-cores may lead to a lack of semantic interpretability of communities. Consequently, this article proposes a method for identifying the optimal k-core with the greatest attribute score in the attribute social network as the target community. The difficulty of the problem is that the query needs to integrate both structural and textual indicators of the community while fully considering the diversity of attribute scoring functions. To effectively reduce computational costs, we incorporate the topological characteristics of the k-core and the attribute characteristics of entities to construct a hierarchical forest. It is worth noting that we name tree nodes in a way similar to pre-order traversal and can maintain the order of all tree nodes during the forest creation process. In such an attribute forest, it is possible to quickly locate the initial solution containing all query vertices and reuse intermediate results during the process of expanding queries. We conducted effectiveness and performance experiments on multiple real datasets. As the results show, attribute scoring functions are not monotonic, and the algorithm proposed in this paper can avoid scores falling into local optima. With the help of the attribute k-core forest, the actual query time of the Advanced algorithm has improved by two orders of magnitude compared to the BaseLine algorithm. In addition, the average F1 score of our target community has increased by 2.04 times and 26.57% compared to ACQ and SFEG, respectively.