  We have recently introduced Forman's discretization of Ricci curvature to the
realm of complex networks. Forman curvature is an edge-based measure whose
mathematical definition elegantly encapsulates the weights of nodes and edges
in a complex network. In this contribution, we perform a comparative analysis
of Forman curvature with other edge-based measures such as edge betweenness,
embeddedness and dispersion in diverse model and real networks. We find that
Forman curvature in comparison to embeddedness or dispersion is a better
indicator of the importance of an edge for the large-scale connectivity of
complex networks. Based on the definition of the Forman curvature of edges,
there are two natural ways to define the Forman curvature of nodes in a
network. In this contribution, we also examine these two possible definitions
of Forman curvature of nodes in diverse model and real networks. Based on our
empirical analysis, we find that in practice the unnormalized definition of the
Forman curvature of nodes with the choice of combinatorial node weights is a
better indicator of the importance of nodes in complex networks.
