# Using Laplacian Spectrum as Graph Feature Representation

arXiv: https://arxiv.org/abs/1912.00735 · HTML: https://mlsanity.com/paper/1912.00735/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Dec 2019.

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

- [Molecular Topological Profile (MOLTOP) -- Simple and Strong Baseline for Molecular Graph Classification](https://mlsanity.com/paper/2407.12136/) (2024)
- [Graph Classification Gaussian Processes via Spectral Features](https://mlsanity.com/paper/2306.03770/) (2023)

## Abstract (arXiv)

Graphs possess exotic features like variable size and absence of natural ordering of the nodes that make them difficult to analyze and compare. To circumvent this problem and learn on graphs, graph feature representation is required. A good graph representation must satisfy the preservation of structural information, with two particular key attributes: consistency under deformation and invariance under isomorphism. While state-of-the-art methods seek such properties with powerful graph neural-networks, we propose to leverage a simple graph feature: the graph Laplacian spectrum (GLS). We first remind and show that GLS satisfies the aforementioned key attributes, using a graph perturbation approach. In particular, we derive bounds for the distance between two GLS that are related to the textitdivergence to isomorphism, a standard computationally expensive graph divergence. We finally experiment GLS as graph representation through consistency tests and classification tasks, and show that it is a strong graph feature representation baseline.