# M-Fibration Theory with Applications to Weighted Graphs

arXiv: https://arxiv.org/abs/2608.25598 · HTML: https://mlsanity.com/paper/2608.25598/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 26 references that are in the map.
- First posted on arXiv 26 Aug 2026.

## Builds on (most cited first, 6 of 6)

- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Tight Lower and Upper Bounds for the Complexity of Canonical Colour Refinement](https://mlsanity.com/paper/1509.08251/) (2015)
- [Dimension Reduction via Colour Refinement](https://mlsanity.com/paper/1307.5697/) (2013)
- [The Role of Fibration Symmetries in Geometric Deep Learning](https://mlsanity.com/paper/2408.15894/) (2024)
- [Optimal Computation in Anonymous Dynamic Networks](https://mlsanity.com/paper/2207.08061/) (2022)

## Abstract (arXiv)

The purpose of this paper is to provide a general, comprehensive, theoretical framework that allows one to deal with fibrations on graphs labelled on a commutative monoid. This is a genuine extension of the theory of graph fibrations (as introduced in "Fibrations of Graphs" [Discrete Math., vol. 243, pp. 21-66, 2002]), that makes it possible to deal with weighted graphs, and also graphs labelled with other algebraic structures. The derived theory also lends itself naturally to consider approximate fibrations. As an example, we show how the derived theory can be applied to the reduction of weighted networks, providing a strong theoretical underpinning to recent empirical results.