Sneddon Lecture: How directed is a directed network?

Professor Robert MacKay, FRS FInstP FIMA (University of Warwick)

Tuesday 21st April, 2020 16:00-17:00 Online Zoom lecture


Many systems can be represented by directed graphs, e.g. food webs, supply networks, social networks, metabolic networks, language networks, financial networks. The nodes represent the objects and a directed edge indicates a flow from one node to another or influence of one node on another.

In some networks, the edges line up in an overall direction; in others, they do not. The old notion of “trophic level” from ecology, and its more recent analogue “upstreamness” in economics, provide one way to quantify this, but they require basal or top nodes and have various other shortcomings.

In joint work with Samuel Johnson and Bazil Sansom, we present an improved notion of trophic level and a resulting notion of trophic coherence. We illustrate their application to a wide variety of real-world networks and we derive some nice mathematical relationships of trophic coherence with other significant network properties like non-normality, stability of contagion processes, and cyclicality.

The work was supported by the Economic and Social Research Council via the Instability hub of the Rebuilding Macroeconomics programme of the National Institute for Economic and Social Research.

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