# Current Flow Group Closeness Centrality for Complex Networks

arXiv: https://arxiv.org/abs/1802.02556 · HTML: https://mlsanity.com/paper/1802.02556/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Feb 2018.

## Built on by (most cited first, 2 of 2)

- [A Fast Algorithm for Moderating Critical Nodes via Edge Removal](https://mlsanity.com/paper/2309.06392/) (2023)
- [Promoting Fairness in Information Access within Social Networks](https://mlsanity.com/paper/2512.14711/) (2025)

## Abstract (arXiv)

Current flow closeness centrality (CFCC) has a better discriminating ability than the ordinary closeness centrality based on shortest paths. In this paper, we extend this notion to a group of vertices in a weighted graph, and then study the problem of finding a subset S of k vertices to maximize its CFCC C(S), both theoretically and experimentally. We show that the problem is NP-hard, but propose two greedy algorithms for minimizing the reciprocal of C(S) with provable guarantees using the monotoncity and supermodularity. The first is a deterministic algorithm with an approximation factor (1-frackk-1·frac1e) and cubic running time; while the second is a randomized algorithm with a (1-frackk-1·frac1e-ε)-approximation and nearly-linear running time for any ε > 0. Extensive experiments on model and real networks demonstrate that our algorithms are effective and efficient, with the second algorithm being scalable to massive networks with more than a million vertices.