Spectrum of Complex Networks: a study via machine learning

• Grant number: 25/03055-8
• Support Opportunities: Scholarships in Brazil - Master
• Start date: July 01, 2025
• End date: June 30, 2027
• Field of knowledge: Physical Sciences and Mathematics - Physics
• Principal Investigator: Francisco Aparecido Rodrigues
• Grantee: Sofia de Freitas Martins
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

Complex networks are graphs composed of vertices interconnected by edges, representing relationships between pairs of objects. These structures are used to describe interactions in complex systems such as social networks, in which vertices are represented by individuals and edges represent some type of social relationship, such as friendship. The spectrum of a network is composed of the eigenvalues of the matrix associated with this network, describing global aspects of connectivity and the dynamics of the system. In this project, machine learning methods will be employed to study network spectra. Specifically, regression models will be fitted to predict structural metrics, such as centrality, using spectral eigenvalues as input. This approach allows us to identify which spectral components are most correlated with topological properties, providing a new perspective for network structural analysis based on the spectrum.