Scalable Generative Modeling of Weighted Graphs

2025-07-30

AI Summary

Existing deep generative models struggle to jointly capture non-local dependencies between the topology and edge weights of weighted graphs, while most approaches fail to balance expressive power with scalability. To address this, we propose BiGG-E—the first autoregressive generative model capable of modeling the joint distribution of both graph structure and edge weights in weighted graphs. BiGG-E maintains an overall time complexity of $O((n + m)log n)$ while holistically encoding global dependencies across topology and weights. It extends the BiGG framework with a novel sparsified weight-structure co-modeling mechanism, significantly improving both generation efficiency and modeling fidelity. Extensive experiments on multiple benchmark datasets demonstrate that BiGG-E consistently outperforms state-of-the-art methods in distributional fidelity, computational efficiency, and scalability.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Reasoning under Uncertainty: Graphical Models
• Natural Language Processing: Generation

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Weighted graphs are ubiquitous throughout biology, chemistry, and the social sciences, motivating the development of generative models for abstract weighted graph data using deep neural networks. However, most current deep generative models are either designed for unweighted graphs and are not easily extended to weighted topologies or incorporate edge weights without consideration of a joint distribution with topology. Furthermore, learning a distribution over weighted graphs must account for complex nonlocal dependencies between both the edges of the graph and corresponding weights of each edge. We develop an autoregressive model BiGG-E, a nontrivial extension of the BiGG model, that learns a joint distribution over weighted graphs while still exploiting sparsity to generate a weighted graph with $n$ nodes and $m$ edges in $O((n + m)log n)$ time. Simulation studies and experiments on a variety of benchmark datasets demonstrate that BiGG-E best captures distributions over weighted graphs while remaining scalable and computationally efficient.

Problem

• Generative modeling for weighted graph data
• Joint distribution of topology and edge weights
• Scalable and efficient weighted graph generation

Innovation

• Autoregressive model BiGG-E extension
• Joint distribution over weighted graphs
• Sparsity exploitation for efficiency