Symmetry and Asymmetry Study in Graph Theory

This Reprint brings together recent studies on symmetry and asymmetry in graph theory, graph learning, and complex network modeling. The collected papers reflect both theoretical and application-oriented developments, including self-supervised graph neural networks for bipartite matching, self-attention-based community detection in heterogeneous networks, graph symmetry cognitive learning for cloud imaging, symmetry-enhanced residual graph convolutional networks for medical image classification, and asymmetric path modeling in equipment maintenance knowledge graphs. The Reprint also extends graph-based and symmetry-inspired methods to phase mask optimization, blockchain-enabled emission control in shipping networks, mechanical drilling speed prediction, and structured label dependency modeling in legal judgment prediction. Together, these contributions show how graph structures, symmetry principles, learning algorithms, and optimization models can support intelligent analysis, robust decision making, and interdisciplinary applications across computer science-, mathematics-, engineering-, healthcare-, and knowledge-based systems.