# Characterization and comparison of large directed graphs through the spectra of the magnetic Laplacian

arXiv: https://arxiv.org/abs/2007.03466 · HTML: https://mlsanity.com/paper/2007.03466/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jul 2020.

## Built on by (most cited first, 7 of 7)

- [MagNet: A Neural Network for Directed Graphs](https://mlsanity.com/paper/2102.11391/) (2021)
- [MSGNN: A Spectral Graph Neural Network Based on a Novel Magnetic Signed Laplacian](https://mlsanity.com/paper/2209.00546/) (2022)
- [Geometric Scattering on Measure Spaces](https://mlsanity.com/paper/2208.08561/) (2022)
- [LightDiC: A Simple yet Effective Approach for Large-scale Digraph Representation Learning](https://mlsanity.com/paper/2401.11772/) (2024)
- [A Graph Convolution for Signed Directed Graphs](https://mlsanity.com/paper/2208.11511/) (2022)
- [Unraveling the graph structure of tabular data through Bayesian and spectral analysis](https://mlsanity.com/paper/2110.01421/) (2021)
- [Beyond symmetrization: effective adjacency matrices and renormalization for (un)singed directed graphs](https://mlsanity.com/paper/2406.01517/) (2024)

## Abstract (arXiv)

In this paper we investigated the possibility to use the magnetic Laplacian to characterize directed graphs (a.k.a. networks). Many interesting results are obtained, including the finding that community structure is related to rotational symmetry in the spectral measurements for a type of stochastic block model. Due the hermiticity property of the magnetic Laplacian we show here how to scale our approach to larger networks containing hundreds of thousands of nodes using the Kernel Polynomial Method (KPM). We also propose to combine the KPM with the Wasserstein metric in order to measure distances between networks even when these networks are directed, large and have different sizes, a hard problem which cannot be tackled by previous methods presented in the literature. In addition, our python package is publicly available at hrefhttps://github.com/stdogpkg/emategithub.com/stdogpkg/emate. The codes can run in both CPU and GPU and can estimate the spectral density and related trace functions, such as entropy and Estrada index, even in directed or undirected networks with million of nodes.