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PERSPECTIVE article

Front. Appl. Math. Stat.
Sec. Mathematical Physics
Volume 10 - 2024 | doi: 10.3389/fams.2024.1512865
This article is part of the Research Topic Quasi-Normal Modes, Non-Selfadjoint Operators and Pseudospectrum: an Interdisciplinary Approach View all 11 articles

The Connection between Non-normality and Trophic Coherence in Directed Graphs

Provisionally accepted
Catherine Drysdale Catherine Drysdale *Samuel Johnson Samuel Johnson
  • University of Birmingham, Birmingham, United Kingdom

The final, formatted version of the article will be published soon.

    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 nonnormality 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 necessaritly represent graphs.

    Keywords: Directed graphs, trophic coherence, non-normality, Pseudospectra, trophic levels, epidemic modelling

    Received: 17 Oct 2024; Accepted: 30 Nov 2024.

    Copyright: © 2024 Drysdale and Johnson. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

    * Correspondence: Catherine Drysdale, University of Birmingham, Birmingham, United Kingdom

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