  Traditionally, network analysis is based on local properties of vertices,
like their degree or clustering, and their statistical behavior across the
network in question. This paper develops an approach which is different in two
respects. We investigate edge-based properties, and we define global
characteristics of networks directly. The latter will provide our affirmative
answer to the question raised in the title. More concretely, we start with
Forman's notion of the Ricci curvature of a graph, or more generally, a
polyhedral complex. This will allow us to pass from a graph as representing a
network to a polyhedral complex for instance by filling in triangles into
connected triples of edges and to investigate the resulting effect on the
curvature. This is insightful for two reasons: First, we can define a curvature
flow in order to asymptotically simplify a network and reduce it to its
essentials. Second, using a construction of Bloch, which yields a discrete
Gauss-Bonnet theorem, we have the Euler characteristic of a network as a global
characteristic. These two aspects beautifully merge in the sense that the
asymptotic properties of the curvature flow are indicated by that Euler
characteristic.
