# Weighted network estimation by the use of topological graph metrics

## TL;DR

This paper introduces an optimization-based approach that uses topological graph metrics to estimate and denoise weighted networks, bridging graph theory, network science, and optimization.

## Contribution

It develops gradient-based methods incorporating graph metrics as priors for network estimation, a novel integration of graph theory into network optimization.

## Key findings

- Effective in denoising and completing networks
- Demonstrated on toy and real-world datasets
- Establishes new links between graph theory and optimization

## Abstract

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.