AUTHOR=Drysdale Catherine , Johnson Samuel 

TITLE=The connection between non-normality and trophic coherence in directed graphs

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=Volume 10 - 2024

YEAR=2025

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2024.1512865

DOI=10.3389/fams.2024.1512865

ISSN=2297-4687

ABSTRACT=Trophic coherence and non-normality are both ways of describing the overall directionality of directed graphs or networks. Trophic coherence can be regarded as a measure of how neatly a graph can be divided into distinct layers, whereas non-normality is a measure of how unlike a matrix is with its transpose. We explore the relationship between trophic coherence and non-normality by first considering the connections that exist in literature and calculating the trophic coherence and non-normality for some toy networks. We then explore how persistence of an epidemic in an SIS model depends on coherence and how this relates to the non-normality. A similar effect on dynamics governed by a linear operator suggests that it may be useful to extend the concept of trophic coherence to matrices, which do not necessarily represent graphs.