  Forman-Ricci curvature (FRC) has become a potent and powerful for analysing
empirical networks, as the distribution of the curvature values can identify
some structural information that is not readily detected by other schemes. For
a graph, it is easy to compute, but it is not sensitive to higher-order
structural information. That issue can be handled by going to the clique
complex of the graph, and in fact, such complexes also emerge as Vietoris-Rips
complexes in Topological Data Analysis. But then, with standard methods, it
becomes much more computationally expensive. In this paper, we therefore
develop a novel set-theoretic formulation for computing such high-order FRC in
complex networks. We provide a pseudo-code, a software implementation coined
FastForman, as well as a benchmark comparison with alternative implementations.
Crucially, our representation theory reveals previous computational bottlenecks
and also accelerates the computation of FRC.

Data Analysis, Statistics and Probability;Discrete Mathematics;Performance;Combinatorics