  In this paper, we study the problem of unsupervised graph representation
learning by harnessing the control properties of dynamical networks defined on
graphs. Our approach introduces a novel framework for contrastive learning, a
widely prevalent technique for unsupervised representation learning. A crucial
step in contrastive learning is the creation of 'augmented' graphs from the
input graphs. Though different from the original graphs, these augmented graphs
retain the original graph's structural characteristics. Here, we propose a
unique method for generating these augmented graphs by leveraging the control
properties of networks. The core concept revolves around perturbing the
original graph to create a new one while preserving the controllability
properties specific to networks and graphs. Compared to the existing methods,
we demonstrate that this innovative approach enhances the effectiveness of
contrastive learning frameworks, leading to superior results regarding the
accuracy of the classification tasks. The key innovation lies in our ability to
decode the network structure using these control properties, opening new
avenues for unsupervised graph representation learning.
