Date of Award

2025-12-01

Degree Name

Doctor of Philosophy

Department

Mathematical Sciences

Advisor(s)

Maria C. Mariani

Abstract

Graph-structured data appear across diverse domains, such as social networks, citation graphs, biological systems, and knowledge bases. Graph Neural Networks (GNNs) have emerged as a powerful framework for learning on such data, yet existing architectures face significant challenges. Graph Convolutional Networks (GCNs) suffer from over-smoothing as depth increases, Graph Attention Networks (GATs) introduce computational and statistical instabilities, and naïve multi-hop propagation inflates memory and computation while failing to adapt to topology. These limitations motivate the development of a new framework that is both expressive and scalable. This dissertation proposes the Multi-Hop Hybrid Graph Neural Network (MHHGNN), a novel architecture that integrates three complementary components: (i) multihop propagation with adaptive, per-node attention, (ii) a GCN branch that provides stable structural smoothing, and (iii) a GAT branch that models semantic neighbor importance. The outputs of these branches are fused into unified node embeddings, which balance structural, semantic, and long-range contextual information. To prevent hop-collapse and enforce robustness, MHHGNN incorporates an entropy regularizer, Laplacian smoothness prior, and parameter norm constraints.

Beyond supervised objectives, this work extends MHHGNN with a contrastive learning module that leverages graph augmentations to align embeddings across perturbed views. This hybrid objective combines classification, smoothness, entropy, and contrastive losses, and enables MHHGNN to effectively exploit both labeled and unlabeled data, improving generalization. Empirical results on benchmark citation datasets (Cora, Citeseer, and PubMed) demonstrate that MHHGNN outperforms state-of-the-art baselines in node classification accuracy while maintaining scalability. In summary, this dissertation advances graph representation learning by introducing a hybrid model that addresses over-smoothing, instability, and inefficiency in existing GNN designs. The proposed MHHGNN establishes a flexible and extensible foundation for future research in graph learning, with potential applications in domains such as biomedical networks, financial risk modeling, and recommendation systems.

Language

en

Provenance

Received from ProQuest

File Size

113 p.

File Format

application/pdf

Rights Holder

James Arthur

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