Characterization of higher-order networks

• Grant number: 25/28128-8
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: February 01, 2026
• End date: January 31, 2027
• Field of knowledge: Physical Sciences and Mathematics - Physics
• Principal Investigator: Guilherme Ferraz de Arruda
• Grantee: Livia Silva Mansano de Moraes
• Host Institution: Instituto de Física Gleb Wataghin (IFGW). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

Complex systems often consist of thousands or even millions of interacting components. In order to understand these systems, we need to use statistical approaches to select and summarize relevant information. When dealing with graphs or networks, we have a large amount of literature. However, for the analysis of higher-order networks, we are still lacking, and many of the methods are just extensions borrowed from the network literature. Thus, the goal of this proposal is to study and develop characterization measures for higher-order networks by first reproducing some literature results and then uncovering information about the structural organization of such systems. Here, our first goal is to explore information-theoretic methods. With our results, we also hope that this exploration will ultimately open up new avenues of investigation. At the end of this proposal, we also hope to apply our results to the study of message communication in hypergraphs. In addition to the scientific results, the student is expected to become familiar with the scientific method and improve his/her academic skills in statistics, linear algebra, and computational methods. (AU)