  Local neighborhoods play a crucial role in embedding generation in
graph-based learning. It is commonly believed that nodes ought to have
embeddings that resemble those of their neighbors. In this research, we try to
carefully expand the concept of similarity from nearby neighborhoods to the
entire graph. We provide an extension of similarity that is based on
transitivity relations, which enables Graph Neural Networks (GNNs) to capture
both global similarities and local similarities over the whole graph. We
introduce Transitivity Graph Neural Network (TransGNN), which more than local
node similarities, takes into account global similarities by distinguishing
strong transitivity relations from weak ones and exploiting them. We evaluate
our model over several real-world datasets and showed that it considerably
improves the performance of several well-known GNN models, for tasks such as
node classification.
