Kemeny Constant-Based Optimization of Network Clustering Using Graph Neural Networks

A New Way to Break Down Complex Networks
Imagine a dynamical network of nodes that could be anything from a social network to conformational states of biological systems. The challenge is to divide this network into smaller, meaningful groups. Traditionally, this clustering task does not use the dynamical timescales inherent to the system, only network edges are taken into account. We introduced a new approach, where we optimize coarse-grained timescales via the Kemeny constant to obtain metastable clustered states. However, this task is computationally highly challenging. In this paper, we explored the use of graph neural networks (GNNs), a deep learning architecture that is particularly good at understanding networks and helps identify the best way to divide a large intractable network into small number of groups using the Kemeny constant. The results were promising. The GNNs were able to divide the networks into groups that made sense based on the properties of the molecules. This could be useful for understanding how different parts of biomolecular systems interact and designing new drugs.

Authors: Sam Alexander Martino, Joao Morado, Chenghao Li, Zhenghao Lu, Edina Rosta