Muhammad Ifte khairul Islam, Tanvir Hossain, Esra Akbas
Graph Contrastive Learning (GCL) has achieved remarkable success in self-supervised representation learning by maximizing agreement between augmented views of a graph. Although augmented view generation is the central step in GCL, existing models rely on stochastic augmentation of the input graph, such as edge perturbation and node masking, which lack structural awareness and frequently destroy critical topology or introduce semantically inconsistent views. While recent adaptive methods improve upon random perturbations, they primarily operate on localized node or edge neighborhoods and fail to capture higher-order, macro-level structural organization crucial for graph classification. To address this limitation, we propose Structure-aware Compression for Graph Contrastive Learning (SAC-GCL), a novel framework that employs structural decomposition and graph compression as a principled view generation strategy. Moving beyond random augmentations, SAC-GCL leverages structural decomposition techniques to extract cohesive subgraphs and condense them into supernodes, constructing coarsened graph views that preserve local density and capture higher-level structural patterns while reducing noise and redundancy. We leverage multiple cohesive subgraph models to derive complementary views of the graph, each capturing distinct structural properties. To capture multi-resolution information, a hierarchical view encoder processes these compressed views by initializing super-node features with shared-weight cohesive subgraph embeddings. Our results from extensive experiments on six benchmark datasets demonstrate that structure-aware compression provides a powerful alternative to random perturbations, yielding more robust and discriminative graph representations for graph classification tasks.
Eigenvalues are a workhorse of graph machine learning: spectral clustering, spectral graph neural networks, and graph kernels all summarize a network by the eigenvalues of a matrix. These eigenvalues are almost always treated as a static list of numbers. When a graph changes, however, its eigenvalues move, and when the matrix is not symmetric, they move in the complex plane, where they can wind around each other. The pattern of this winding is a braid, a classical object from topology. We propose spectral braids, a methodology for dynamic directed networks: each snapshot is aggregated into a community-level transition matrix, its complex eigenvalues are tracked over time, and the braid they trace is read off as a word. The word is then mapped to a matrix by the Burau representation, which gives a fixed-size feature vector for any classifier. The braid has a concrete meaning: each eigenvalue describes how a group of communities behaves, and each crossing records one group overtaking another. We evaluate the method on dynamic network classification, using synthetic networks of online communities whose labels describe how the network evolved between the same starting and ending states. Our experimental results show that the proposed features reach 97.1% accuracy on four classes, against 44.5% for the best feature set that does not track eigenvalues, and that the Burau features also separate networks containing the same events in a different order, which simple counts of crossings cannot do. To the best of our knowledge, this is the first study that defines braids and braid monodromy on graph data and uses them as features for learning on dynamic networks.