function. Structural information is not encoded by the nodes, but by the relations between them.

These relations are expressed in edges that possess properties like direction and weight. In this

work, we want to explore the space of graphs with a given Ricci curvature sequence which is an

edge-based classifier. Having its roots in differential geometry, several discrete Ricci curvatures

have been shown to capture geometrical properties of graphs and have been successfully applied

to complex networks.

In this talk, we want to explore the space of graphs with a given discrete Ricci curvature sequence.

For this, we will first analyse a graph ensemble created by a Markov Chain Monte Carlo type

algorithm approximating a given curvature sequence. Second, we will obtain theoretical results

on the collection of all graphs with a fixed curvature and degree sequence for the simple notion

of Forman–Ricci curvature and see that these graphs are connected by a set of ‘moves’.