Abstract
The magnitude of a graph is one of a family of cardinalitylike invariants extending across mathematics; it is a cousin to Euler characteristic and geometric measure. Among its cardinalitylike properties are multiplicativity with respect to cartesian product and an inclusionexclusion formula for the magnitude of a union. Formally, the magnitude of a graph is both a rational function over Q and a power series over Z. It shares features with one of the most important of all graph invariants, the Tutte polynomial; for instance, magnitude is invariant under Whitney twists when the points of identification are adjacent. Nevertheless, the magnitude of a graph is not determined by its Tutte polynomial, nor even by its cycle matroid, and it therefore carries information that they do not.
Original language  English 

Pages (fromto)  247264 
Number of pages  19 
Journal  Mathematical Proceedings of The Cambridge Philosophical Society 
Volume  166 
Issue number  2 
Early online date  27 Nov 2017 
DOIs  
Publication status  Published  Mar 2019 
Fingerprint
Dive into the research topics of 'The magnitude of a graph'. Together they form a unique fingerprint.Profiles

Tom Leinster
 School of Mathematics  Personal Chair of Category Theory
Person: Academic: Research Active