RRWK: Structural and Computational Bounds for Dense Graph Subgraph Extraction

Subgraph extraction constitutes a key component of graph representation learning, enabling scalable analysis and downstream inference over large and complex networks. Nevertheless, existing local extraction approaches frequently exhibit substantial performance degradation in dense graph regimes, where excessive neighborhood expansion and the loss of structural cohesion negatively affect both computational tractability and representational fidelity. Recent work has reformulated the subgraph extraction task in this problem as a local clustering procedure based on a personalized PageRank. However, despite obtaining better results, this approach is affected by the density of the network, limiting its results to networks with medium-low density. In this work, we introduce return random walk kinship (RRWK), a density-aware subgraph extraction framework based on bounded outbound and return random-walk connectivity. The proposed method preserves structurally cohesive regions by exploiting alternative return paths capable of jointly capturing local and global organizational properties of the graph. In contrast to conventional enclosing-subgraph and personalized PageRank-based strategies, RRWK is specifically designed to maintain structural robustness as graph density increases. Furthermore, we study the structural and computational bounds of the proposed method. Experimental results on both synthetic and real-world datasets demonstrate that RRWK consistently preserves the structural properties of the original graph more accurately than state-of-the-art subgraph extraction baselines, while maintaining competitive computational performance in dense graph scenarios.