# Fixed-Point Centrality for Networks

arXiv: https://arxiv.org/abs/2209.07070 · HTML: https://mlsanity.com/paper/2209.07070/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 49 references that are in the map.
- First posted on arXiv 15 Sep 2022.

## Builds on (most cited first, 14 of 14)

- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Implicit Deep Learning](https://mlsanity.com/paper/1908.06315/) (2019)
- [Graphon Neural Networks and the Transferability of Graph Neural Networks](https://mlsanity.com/paper/2006.03548/) (2020)
- [Implicit Graph Neural Networks](https://mlsanity.com/paper/2009.06211/) (2020)
- [Robust Implicit Networks via Non-Euclidean Contractions](https://mlsanity.com/paper/2106.03194/) (2021)
- [Centrality measures for graphons: Accounting for uncertainty in networks](https://mlsanity.com/paper/1707.09350/) (2017)
- [Fixed Point Strategies in Data Science](https://mlsanity.com/paper/2008.02260/) (2020)
- [Graphon Mean Field Games and the GMFG Equations](https://mlsanity.com/paper/2008.10216/) (2020)
- [Centrality Measures in Networks](https://mlsanity.com/paper/1608.05845/) (2016)
- [LQG Graphon Mean Field Games: Analysis via Graphon Invariant Subspaces](https://mlsanity.com/paper/2004.00679/) (2020)
- [Centrality with Diversity](https://mlsanity.com/paper/2101.07371/) (2021)
- [Centrality-Weighted Opinion Dynamics: Disagreement and Social Network Partition](https://mlsanity.com/paper/2104.03485/) (2021)

## Abstract (arXiv)

This paper proposes a family of network centralities called fixed-point centralities. This centrality family is defined via the fixed point of permutation equivariant mappings related to the underlying network. Such a centrality notion is immediately extended to define fixed-point centralities for infinite graphs characterized by graphons. Variation bounds of such centralities with respect to the variations of the underlying graphs and graphons under mild assumptions are established. Fixed-point centralities connect with a variety of different models on networks including graph neural networks, static and dynamic games on networks, and Markov decision processes.