Advancements in Network Statistics: extensions to HPC and hypergraphs.

• Grant number: 24/03261-4
• Support Opportunities: Regular Research Grants
• Start date: February 01, 2025
• End date: January 31, 2028
• Field of knowledge: Physical Sciences and Mathematics - Computer Science - Computational Mathematics
• Principal Investigator: André Fujita
• Grantee: André Fujita
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated researchers: Daniel Yasumasa Takahashi ; João Ricardo Sato
• Associated research grant(s): 24/09195-3 - A spectral distribution approximation algorithm for network time series, AP.R
• Associated scholarship(s): 25/02549-7 - Development of software for estimating the spectral density of large networks using HPC., BP.TT

Abstract

Networks pervade various domains, from molecular biology to social networks. However, empirical networks often exhibit stochastic behavior, challenging traditional graph theory-based approaches. Traditional approaches relying on graph theory face limitations in capturing the stochastic nature of empirical networks, motivating the need for alternative methodologies. Graph neural networks offer promising predictive accuracy but lack interpretability. In contrast, probabilistic models and statistical tools based on network invariants provide a framework for understanding complex network behavior. The network spectral density (NSD) emerges as an invariant for network characterization, but its computational cost limits scalability. We propose GPU-based implementations and algorithmic optimizations to enable efficient analysis of billion-node networks. Additionally, we highlight the necessity of extending statistical methods to hypergraphs, which offer a more natural representation of specific biological networks. Our proposed methodologies have broad applications, ranging from neuroscience to public policy. By enabling analysis of large-scale networks, including billion-node networks and hypergraphs, we unlock new avenues for understanding complex systems and identifying critical patterns. In conclusion, this proposal advances network analysis methodologies, bridging the gap between theoretical frameworks and practical applications in real-world complex systems. (AU)