Characterization and comparison of large directed networks through the spectra of the magnetic Laplacian

Author(s)

de Resende, Bruno Messias F. ^[1] ; Costa, Luciano da F. ^[1]

Affiliation

^[1] Univ Sao Paulo, Inst Fis Sao Carlos, BR-13566590 Sao Carlos, SP - Brazil

• Document type: Journal article
• Source: Chaos; v. 30, n. 7 JUL 2020.
• Web of Science Citations: 0

Abstract

In this paper, we investigated the possibility of using the magnetic Laplacian to characterize directed networks. We address the problem of characterization of network models and perform the inference of the parameters used to generate these networks under analysis. Many interesting results are obtained, including the finding that the 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), a method commonly used in condensed matter physics. Using a combination of KPM with the Wasserstein metric, we show how we can measure distances between networks, even when these networks are directed, large, and have different sizes, a hard problem that cannot be tackled by previous methods presented in the literature. (AU)

• FAPESP's process: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry
• Grantee: Francisco Louzada Neto
• Support Opportunities: Research Grants - Research, Innovation and Dissemination Centers - RIDC
• FAPESP's process: 15/22308-2 - Intermediate representations in Computational Science for knowledge discovery
• Grantee: Roberto Marcondes Cesar Junior
• Support Opportunities: Research Projects - Thematic Grants