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Trophic analysis of directed networks

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In nature, large, densely interconnected ecosystems such as rainforests or coral reefs are particularly stable – but this, as Lord May famously showed, looks mathematically paradoxical. A topological property of directed networks which we called ‘trophic coherence’ may account for this phenomenon, as well as many other interesting features of complex systems [1,2]. In recent years trophic coherence has been related to graph eigenspectra, non-normality, stability and percolation, and applied to finance, power structures, deep neural networks and train lines [3,4]. I will summarise where this research is at the moment, and the many open questions which are emerging.


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

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

[3] S. Johnson, ‘Digraphs are different: Why directionality matters in complex systems’, Journal of Physics: Complexity, 1, 015003 (2020)

[4] R.S. MacKay, S. Johnson, B. Sansom, ‘How directed is a directed network?’, Royal Society Open Science 7: 201138 (2020)

This talk is part of the Study group in Graph Theory, Topology and Algorithms series.

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