$\beta$-diversity and Graph Sheaf Laplacians

Abstract

We suggest an approach to measuring biodiversity based on the spectrum of graph sheaf Laplacians associated with the sample data. In particular, we define a ${\beta }_{ss}$, a genuine generalisation of the multiplicative $\beta$-diversity. This scalar quantity is easily computable using methods of linear algebra. We show using simple examples that the notions we introduce (energies $E_k$ and ${\beta }_{ss}$) contain more information than just $\beta$-diversity.

arXiv comment12 pages