Many real-world relationships can be effectively represented as edge-labeled graphs, where edge labels encode semantic information vital for graph computations. Analyzing communities within such graphs is of great importance, with cohesive subgraph queries being a fundamental problem in graph analysis. Among these, the k-core model is one of the most widely studied frameworks for cohesive subgraph queries and has attracted significant attention over the past decade. However, most existing k-core models disregard edge labels, limiting their applicability to semantic-aware analyses. In this paper, we propose an index-based method to address the problem of querying k-cores with label constraints in edge-labeled graphs. We first introduce a basic index that maintains core decomposition results for each possible label set. Then, to further optimize performance, we propose an advanced index structure that captures the label containment properties of k- cores by computing canonical label sets for each possible$k$and each vertex. This approach can greatly reduce the index size while ensuring efficient query processing. We also design an optimized algorithm for constructing our index, achieving a significantly faster runtime than naive construction methods. Extensive experiments on real graphs demonstrate the efficiency and effectiveness of our index-based algorithms.

Bipartite graphs are ubiquitous, such as E-commerce network and gene networks. Efficient analysis of (p, q)- biclique is one of the important problems over bipartite graphs. However, existing works over (p, q)-biclique suffer from two main challenges. Firstly, most of them only focus on static graphs, while lots of bipartite graph-structured data are constantly created in real world, forming streaming bipartite graphs. Secondly, results of (p, q)-biclique could be of exponential scale, which may overwhelm analysts. Hence, computing top$k$most important (p, q)-bicliques is worth considering. In this paper, we study a new problem to maintain top$k$densest (p, q)-bicliques over a streaming bipartite graph. We propose a new framework, called as TopK-BC, to compute the proposed problem effectively. We design an efficient pruning strategy for edge deletion stage, called IDpruning. In particular, we maintain an intermediate density for each edge to efficiently compute high-density (p, q)-bicliques. Also, we introduce effective optimization technologies to filter out unpromising intermediate results and further enhance the performance. Extensive experiments over real world datasets confirm the efficiency and effectiveness of our solution.