# A novel approach to graph distinction through GENEOs and permutants

arXiv: https://arxiv.org/abs/2406.08045 · HTML: https://mlsanity.com/paper/2406.08045/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 31 references that are in the map.
- First posted on arXiv 12 Jun 2024.

## Builds on (most cited first, 13 of 13)

- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Harmonic Networks: Deep Translation and Rotation Equivariance](https://mlsanity.com/paper/1612.04642/) (2016)
- [On the equivalence between graph isomorphism testing and function approximation with GNNs](https://mlsanity.com/paper/1905.12560/) (2019)
- [A Survey on The Expressive Power of Graph Neural Networks](https://mlsanity.com/paper/2003.04078/) (2020)
- [Understanding Deep Convolutional Networks](https://mlsanity.com/paper/1601.04920/) (2016)
- [Geometric Deep Learning and Equivariant Neural Networks](https://mlsanity.com/paper/2105.13926/) (2021)
- [Towards a topological-geometrical theory of group equivariant non-expansive operators for data analysis and machine learning](https://mlsanity.com/paper/1812.11832/) (2018)
- [On Invariance and Selectivity in Representation Learning](https://mlsanity.com/paper/1503.05938/) (2015)
- [On the finite representation of group equivariant operators via permutant measures](https://mlsanity.com/paper/2008.06340/) (2020)
- [Generalized Permutants and Graph GENEOs](https://mlsanity.com/paper/2206.14798/) (2022)
- [Position paper: Towards an observer-oriented theory of shape comparison](https://mlsanity.com/paper/1603.02008/) (2016)

## Built on by (most cited first, 4 of 4)

- [Mathematical Foundation of Interpretable Equivariant Surrogate Models](https://mlsanity.com/paper/2503.01942/) (2025)
- [GENEOnet: Statistical analysis supporting explainability and trustworthiness](https://mlsanity.com/paper/2503.09199/) (2025)
- [Reconstruction of SINR Maps from Sparse Measurements using Group Equivariant Non-Expansive Operators](https://mlsanity.com/paper/2507.19349/) (2025)
- [An Algebraic Representation Theorem for Linear GENEOs in Geometric Machine Learning](https://mlsanity.com/paper/2601.03910/) (2026)

## Abstract (arXiv)

The theory of Group Equivariant Non-Expansive Operators (GENEOs) was initially developed in Topological Data Analysis for the geometric approximation of data observers, including their invariances and symmetries. This paper departs from that line of research and explores the use of GENEOs for distinguishing r-regular graphs up to isomorphisms. In doing so, we aim to test the capabilities and flexibility of these operators. Our experiments show that GENEOs offer a good compromise between efficiency and computational cost in comparing r-regular graphs, while their actions on data are easily interpretable. This supports the idea that GENEOs could be a general-purpose approach to discriminative problems in Machine Learning when some structural information about data and observers is explicitly given.