Networks—as mathematical representations of interconnected units—are relevant in a wide range of real-wold systems, ranging from spreading of diseases along social networks to interconnected neural cells in the brain. Traditionally, networks have been equated with the mathematical concept of a graph that specifies relations between pairs of individual units. While this approach has produced for example powerful tools to analyze data, there has been a shift to recognize the importance of relations and interactions beyond pairs, namely relations between more than two individual units.
In the paper "What are higher-order networks?" published recently in SIAM Review (doi:10.1137/21M1414024), VU mathematician C Bick and coauthors take account of these recent developments from a mathematical perspective. They provide a unified perspective on recent research where nonpairwise interactions play a role. These range from topological data analysis to network dynamical systems, thereby connecting different research directions of interest to the Department of Mathematics at the VU.
Reference: C. Bick, E. Gross, H. A. Harrington, and M. T. Schaub. What Are Higher-Order Networks? SIAM Rev. 65, 686–731 (2023).