The magnitude of a graph
By Tom Leinster. Mathematical Proceedings of the Cambridge Philosophical Society, 2014
55 citations recorded by the source corpus.
Abstract The magnitude of a graph is one of a family of cardinality-like invariants extending across mathematics; it is a cousin to Euler characteristic and geometric measure. Among its cardinality-like properties are multiplicativity with respect to cartesian product and an inclusion-exclusion 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.
Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/7cdac1796b3bb66b73d12bec3efaa60c8c7eadf3
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Citations in the corpus
- Maximizing diversity in biology and beyond (2015, unknown): “For instance, it automatically produces a notion of the Euler characteristic of an (ordinary) category, closely related to topological Euler characteristic [22]; in the context of metric spaces, magnitude encodes geometric information such as volume and dimension [2, 31, 41]; in graph theory, magnit”
- Categorifying the magnitude of a graph (2015, background): “We will see below that various properties of magnitude described by Leinster in [11] are shadows of properties of magnitude homology.”