# Efficient Computation of the Shapley Value for Game-Theoretic Network Centrality

arXiv: https://arxiv.org/abs/1402.0567 · HTML: https://mlsanity.com/paper/1402.0567/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Feb 2014.

## Built on by (most cited first, 14 of 14)

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- [On the Complexity of SHAP-Score-Based Explanations: Tractability via Knowledge Compilation and Non-Approximability Results](https://mlsanity.com/paper/2104.08015/) (2021)
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- [Rethinking Weakly-supervised Video Temporal Grounding From a Game Perspective](https://mlsanity.com/paper/2605.26441/) (2026)
- [Variable importance without impossible data](https://mlsanity.com/paper/2205.15750/) (2022)
- [MaxShapley: Towards Incentive-compatible Generative Search with Fair Context Attribution](https://mlsanity.com/paper/2512.05958/) (2025)
- [Shapley Pruning for Neural Network Compression](https://mlsanity.com/paper/2407.15875/) (2024)
- [FW-Shapley: Real-time Estimation of Weighted Shapley Values](https://mlsanity.com/paper/2503.06602/) (2025)
- [Towards a more efficient computation of individual attribute and policy contribution for post-hoc explanation of cooperative multi-agent systems using Myerson values](https://mlsanity.com/paper/2212.03041/) (2022)
- [Using Cooperative Game Theory to Prune Neural Networks](https://mlsanity.com/paper/2311.10468/) (2023)
- [Causal SHAP: Feature Attribution with Dependency Awareness through Causal Discovery](https://mlsanity.com/paper/2509.00846/) (2025)
- [Local Shapley: Model-Induced Locality and Optimal Reuse in Data Valuation](https://mlsanity.com/paper/2603.03672/) (2026)
- [InfluenceNet: AI Models for Banzhaf and Shapley Value Prediction](https://mlsanity.com/paper/2503.08381/) (2025)
- [Tourist arrival forecasting with game-theoretic social influence weighting and deep learning](https://mlsanity.com/paper/2507.03411/) (2025)

## Abstract (arXiv)

The Shapley value---probably the most important normative payoff division scheme in coalitional games---has recently been advocated as a useful measure of centrality in networks. However, although this approach has a variety of real-world applications (including social and organisational networks, biological networks and communication networks), its computational properties have not been widely studied. To date, the only practicable approach to compute Shapley value-based centrality has been via Monte Carlo simulations which are computationally expensive and not guaranteed to give an exact answer. Against this background, this paper presents the first study of the computational aspects of the Shapley value for network centralities. Specifically, we develop exact analytical formulae for Shapley value-based centrality in both weighted and unweighted networks and develop efficient (polynomial time) and exact algorithms based on them. We empirically evaluate these algorithms on two real-life examples (an infrastructure network representing the topology of the Western States Power Grid and a collaboration network from the field of astrophysics) and demonstrate that they deliver significant speedups over the Monte Carlo approach. For instance, in the case of unweighted networks our algorithms are able to return the exact solution about 1600 times faster than the Monte Carlo approximation, even if we allow for a generous 10% error margin for the latter method.