## The magnitude of a graph

### Tom Leinster – 24 July 2013

Many invariants of size in mathematics - from cardinality to Euler characteristic to (conjecturally) geometric measure - are tied together by the notion of the magnitude of an enriched category. I will give a brief overview of the big picture, before concentrating on one hitherto neglected part of it: the magnitude of a graph. This invariant assigns to each graph a rational function. Not much is known about it yet; in some ways it resembles the Tutte polynomial, but it can distinguish certain graphs that the Tutte polynomial cannot. This is work in progress, with important contributions from David Speyer and Simon Willerton

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