  We provide an overview of Forman-Ricci curvature and persistent homology, and
how their combination can be applied to the study of networks. We discuss how
the usually employed augmented Forman-Ricci curvature formula, only valid for
quasiconvex augmented networks, can be extended to the non-quasiconvex case. We
apply three versions of quasiconvex Forman-Ricci curvature (plain,
triangle-augmented, and pentagon-augmented) to build time filtrations on
non-quasiconvex networks, both model and real-world. Our results suggest that
triangle-augmented curvature should be used until the non-quasiconvex formula
is further studied, as plain curvature omits too much information, and
quasiconvex pentagon-augmented curvature is too rough of an approximation and
significantly distorts the results.
