Statistical modeling of high-order interactions: recent developments and future challenges

C. Matias${}^{a,b,c}$

${}^a$Centre National de la Recherche Scientifique, ${}^b$Sorbonne Université, ${}^c$Université Paris Cité, France

The growing interest in modeling high-order interactions (HOIs) arises from the acknowledgement that many phenomena are fundamentally more complex than what pairwise relationships alone can capture. While networks and their mathematical representation as graphs capture interactions between pairs of entities, HOI are inherently of a different nature, as they may involve the interaction of more than two elements. Taking into account HOI offers a richer and more expressive way to model complex dependencies and interactions across diverse fields, ranging from social network analysis or co-authorship relations, to ecological systems, neurosciences or even chemistry.

In this talk, we will provide an overview of recent advances in the statistical modeling of HOIs, with a particular focus on hypergraphs and the limitations inherent in graph-based representations. We will address the key issues posed by HOIs in comparison to their pairwise counterparts. Additionally, we will explore the challenges associated with node clustering and the definition of communities within this framework.

Keywords: Hypergraphs, node clustering.