Strong Transitivity Relations and Graph Neural Networks
Yassin Mohamadi, Mostafa Haghir Chehreghani
TL;DR
The paper tackles the limitation of traditional GNNs that focus on local neighborhoods by introducing a transitivity-aware framework, TransGNN, to capture global similarities across the entire graph. It constructs a transitivity graph reflecting strong transitivity relations via SimRank and clips weak relations through clustering, then trains a bipartite GNN with shared weights on the original and transitivity graphs. The method combines supervised and unsupervised losses on both graphs, e.g., $\mathcal{L}^{sup} = \mathcal{L}_G^{sup} + \mathcal{L}_{G'}^{sup}$, and their unsupervised counterparts, to enforce alignment between local and global patterns. Empirically, TransGNN improves several GNN backbones (GCN, GAT, GATv2, SGN) on diverse datasets, demonstrates robustness to edge noise, and is supported by ablation studies showing the positive impact of jointly using trans_loss and sim_loss with the base loss.
Abstract
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.