Efficient Approximation Algorithms for Resolvent Subgraph Centrality on Signed Graphs

Node centrality is one of the most fundamental metrics in network science. One notion of centrality that has garnered significant popularity, due to its ability to capture complex local and global structures, is the resolvent subgraph centrality. For a node i, this measures the weighted sum of the number of closed walks starting and ending at i. We first provide a natural and intuitive generalization of resolvent subgraph centrality to cover the larger class of signed graphs. As our main contribution, we present two scalable approximation algorithms: SOLVERRSC, which leverages a linear equation solver, and SIMPLERSC, which utilizes a novel rooted forest sampling technique. We then provide the algorithms GROUPRSC and NEIGHBORRSC, which achieve better accuracy by extracting richer information from sampled forests. Finally, we conduct an extensive set of experiments to validate the accuracy and efficiency of the proposed algorithms. Our code is available at https://github.com/SunYubo23/SignedRSC.