GraphFLEx: Structure Learning Framework for Large Expanding Graphs

TL;DR

GraphFLEx addresses the challenge of learning graph structure on large expanding graphs by enabling incremental updates without full relearning. It unifies clustering, coarsening, and structure learning to focus edge formation on structurally relevant subsets, using mechanisms such as LSH-based coarsening and partition-guided projection, and supports $48$ configurations with theoretical guarantees on edge recovery and runtime. Empirically, it delivers state-of-the-art performance across $26$ datasets and multiple GNN architectures while achieving near-linear scalability, including on graphs with up to millions of nodes. This framework offers a practical pathway for scalable graph structure learning in dynamic environments, with potential extensions to heterophilic graphs and supervised GSL.

Abstract

Graph structure learning is a core problem in graph-based machine learning, essential for uncovering latent relationships and ensuring model interpretability. However, most existing approaches are ill-suited for large-scale and dynamically evolving graphs, as they often require complete re-learning of the structure upon the arrival of new nodes and incur substantial computational and memory costs. In this work, we propose GraphFLEx: a unified and scalable framework for Graph Structure Learning in Large and Expanding Graphs. GraphFLEx mitigates the scalability bottlenecks by restricting edge formation to structurally relevant subsets of nodes identified through a combination of clustering and coarsening techniques. This dramatically reduces the search space and enables efficient, incremental graph updates. The framework supports 48 flexible configurations by integrating diverse choices of learning paradigms, coarsening strategies, and clustering methods, making it adaptable to a wide range of graph settings and learning objectives. Extensive experiments across 26 diverse datasets and Graph Neural Network architectures demonstrate that GraphFLEx achieves state-of-the-art performance with significantly improved scalability.

Figures (13)

• Figure 1: High computational time required to learn graph structures using existing methods, whereas GraphFLEx effectively controls computational growth, achieving near-linear scalability. Notably, Vanilla KNN failed to construct graph structures for more than 10K nodes due to memory limitations.
• Figure 2: This figure illustrates the general pipeline of GraphFLEx, designed to efficiently handle both a) large datasets with missing structure and b) expanding graphs. Both scenarios can be modeled as expanding graphs (details in Section \ref{['sec:large_dynamic']}). GraphFLEx processes a graph ($\mathcal{G}_{t}$) and incoming nodes ($\mathcal{E}_{t+1}$) at time $t$, newly arriving nodes are shown with different timestamps and shades of blue to indicate their arrival time. Our framework comprises of three main components: i) Clustering, which infers $\mathcal{E}_{t+1}$ nodes to existing communities using a pre-trained model $\mathcal{M}_{\text{clust}}(\mathcal{G}_0)$ into smaller, more manageable communities; ii) Since these communities may still be large, a Coarsening, module is applied to further reduce their size while preserving essential structural information; and iii) Finally, a Learning module, where the structure associated with $\mathcal{E}_{t+1}$ nodes are learned using the coarsened graph, followed by projecting this structure onto the $\mathcal{G}_{t}$ graph to create graph $\mathcal{G}_{t+1}$.
• Figure 3: The versatility of GraphFlex in supporting multiple GSL methods.
• Figure 4: Figures (a), (b), and (c) illustrate the growing structure learned using GraphFLEx for HE synthetic dataset. Figures (d), (e), and (f) illustrate the learned structure on Zachary’s karate dataset when existing methods are employed with GraphFLEx. New nodes are denoted using black color.
• Figure 5: Effectiveness of our framework in learning structure between similar MNIST digits and GloVe embeddings.

Theorems & Definitions (9)

• Remark 1
• Remark 2
• Lemma 1
• Remark 3
• Definition 1
• Theorem 1
• proof
• Remark 4
• Theorem 2