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

Catherine Drysdale; Samuel Johnson

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arXiv · 2412.01847

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

Catherine Drysdale·Samuel Johnson

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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 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.

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Catherine Drysdale, Samuel Johnson. 2024-11-27. The connection between non-normality and trophic coherence in directed graphs. https://arxiv.org/abs/2412.01847

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