University of Birmingham > Talks@bham > Combinatorics and Probability Seminar > The trophic structure of directed graphs

The trophic structure of directed graphs

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  • UserSamuel Johnson (University of Birmingham)
  • ClockTuesday 09 January 2018, 15:00-16:00
  • HousePhysics West 106.

If you have a question about this talk, please contact Allan Lo.

Directed graphs can be characterised by their ‘trophic structure’—that is, the patterns observed when vertices are assigned ‘trophic levels’ (as ecologists do with species in food webs) [1]. It has recently been shown using random graph ensembles that this structure, and in particular a quantity called ‘trophic coherence’, can be related to the distributions of directed cycles and adjacency matrix eigenvalues [2]. This, in turn, has important effects on other properties of systems of interacting elements, such as percolation in certain processes or the stability of dynamical systems [3]. I will summarise this work and consider some open questions.

[1] S. Johnson, V. Domínguez-García, L. Donetti, and M.A. Muñoz, Trophic coherence determines food-web stability, PNAS 111 , 17923 (2014) arXiv:1404.7728

[2] S. Johnson and N.S. Jones, Looplessness in networks is linked to trophic coherence, PNAS 114 , 5618 (2017) arXiv:1505.07332

[3] J. Klaise and S. Johnson, From neurons to epidemics: How trophic coherence affects spreading processes, Chaos 26, 065310 (2016) arXiv:1603.00670

This talk is part of the Combinatorics and Probability Seminar series.

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