  Topological metrics of graphs provide a natural way to describe the prominent
features of various types of networks. Graph metrics describe the structure and
interplay of graph edges and have found applications in many scientific fields.
In this work, graph metrics are used in network estimation by developing
optimisation methods that incorporate prior knowledge of a network's topology.
The derivatives of graph metrics are used in gradient descent schemes for
weighted undirected network denoising, network completion, and network
decomposition. The successful performance of our methodology is shown in a
number of toy examples and real-world datasets. Most notably, our work
establishes a new link between graph theory, network science and optimisation.
