The connection between non-normality and trophic coherence in directed graphs
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 t...
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| Format: | Article |
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Frontiers Media S.A.
2025-01-01
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| Series: | Frontiers in Applied Mathematics and Statistics |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fams.2024.1512865/full |
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| author | Catherine Drysdale Samuel Johnson |
| author_facet | Catherine Drysdale Samuel Johnson |
| author_sort | Catherine Drysdale |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ad7786d554d54f49949dc794a29dfa9f |
| institution | Kabale University |
| issn | 2297-4687 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Applied Mathematics and Statistics |
| spelling | doaj-art-ad7786d554d54f49949dc794a29dfa9f2025-01-07T06:50:05ZengFrontiers Media S.A.Frontiers in Applied Mathematics and Statistics2297-46872025-01-011010.3389/fams.2024.15128651512865The connection between non-normality and trophic coherence in directed graphsCatherine Drysdale0Samuel Johnson1Centre for Systems Modelling and Quantitative Biomedicine, University of Birmingham, Edgbaston, United KingdomSchool of Mathematics, University of Birmingham, Edgbaston, United KingdomTrophic 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.https://www.frontiersin.org/articles/10.3389/fams.2024.1512865/fulldirected graphstrophic coherencenon-normalitypseudospectratrophic levelsepidemic modeling |
| spellingShingle | Catherine Drysdale Samuel Johnson The connection between non-normality and trophic coherence in directed graphs Frontiers in Applied Mathematics and Statistics directed graphs trophic coherence non-normality pseudospectra trophic levels epidemic modeling |
| title | The connection between non-normality and trophic coherence in directed graphs |
| title_full | The connection between non-normality and trophic coherence in directed graphs |
| title_fullStr | The connection between non-normality and trophic coherence in directed graphs |
| title_full_unstemmed | The connection between non-normality and trophic coherence in directed graphs |
| title_short | The connection between non-normality and trophic coherence in directed graphs |
| title_sort | connection between non normality and trophic coherence in directed graphs |
| topic | directed graphs trophic coherence non-normality pseudospectra trophic levels epidemic modeling |
| url | https://www.frontiersin.org/articles/10.3389/fams.2024.1512865/full |
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