Fast Maximization of Current Flow Group Closeness Centrality

Derived from effective resistances, the current flow closeness centrality (CFCC) for a group of nodes measures the importance of node groups in an undirected graph with $n$ nodes. Given the widespread applications of identifying crucial nodes, we investigate the problem of maximizing CFCC for a node group $S$ subject to the cardinality constraint $|S|=k\ll n$. Despite the proven NP-hardness of this problem, we propose two novel greedy algorithms for its solution. Our algorithms are based on spanning forest sampling and Schur complement, which exhibit nearly linear time complexities and achieve an approximation factor of $1-\frac{k}{k-1}\frac{1}{\mathrm{e}}-\epsilon$ for any $0<\epsilon<1$. Extensive experiments on real-world graphs illustrate that our algorithms outperform the state-of-the-art method in terms of efficiency and effectiveness, scaling to graphs with millions of nodes.