  In the context of machine learning for graphs, many researchers have
empirically observed that Deep Graph Networks (DGNs) perform favourably on node
classification tasks when the graph structure is homophilic (\ie adjacent nodes
are similar). In this paper, we introduce Lying-GCN, a new DGN inspired by
opinion dynamics that can adaptively work in both the heterophilic and the
homophilic setting. At each layer, each agent (node) shares its own opinions
(node embeddings) with its neighbours. Instead of sharing its opinion directly
as in GCN, we introduce a mechanism which allows agents to lie. Such a
mechanism is adaptive, thus the agents learn how and when to lie according to
the task that should be solved. We provide a characterisation of our proposal
in terms of dynamical systems, by studying the spectral property of the
coefficient matrix of the system. While the steady state of the system
collapses to zero, we believe the lying mechanism is still usable to solve node
classification tasks. We empirically prove our belief on both synthetic and
real-world datasets, by showing that the lying mechanism allows to increase the
performances in the heterophilic setting without harming the results in the
homophilic one.
