We propose a model allowing to generate graphs of a chosen number of nodes and expected number of edges, following an arbitrary structure, and with a controllable amount of randomness. The model requires: • The number of nodes n • The expected number of edges m • A cost function describing the generated network’s structure Let’s take a simple example: a possible cost function for a spatial graph is simply the distance betwen the nodes —This distance can be attributed randomly, or kept from observed data.