$β$-diversity and Graph Sheaf Laplacians

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 $β_{ss}$, a genuine generalisation of the multiplicative $β$-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 $β_{ss}$) contain more information than just $β$-diversity.