2024/11/27 by Catherine Drysdale, Drysdale, Catherine, Samuel Johnson +1
Computer Science · Materials Science · Neuroscience · #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Photoreceptor and optogenetics research #Physics and Society (physics.soc-ph) #Statistical Mechanics (cond-mat.stat-mech) #Supramolecular Self-Assembly in Materials
paper · pdf · doi:10.48550/arxiv.2412.01847
openalex publication_date 2024/11/27 · openalex created_date 2024/12/06 · openalex updated_date 2026/07/28
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 the 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.