GraphWeave: Interpretable and Robust Graph Generation via Random Walk Trajectories

2025-09-21

AI Summary

Existing diffusion-based methods for generating novel graphs from unknown graph families suffer from uninterpretable distortions in embedding space or poor controllability over multi-step structural evolution in discrete space. Method: We propose a two-stage interpretable graph generation framework: (1) modeling intrinsic graph patterns—e.g., community structure and PageRank distribution—via random-walk trajectory representation; and (2) jointly optimizing edge structures for robust graph reconstruction. Our approach integrates a trajectory-aware Transformer with end-to-end joint training, avoiding embedding distortion and discrete structural jumps. Contribution/Results: Evaluated on four synthetic and five real-world datasets, our method achieves statistically significant improvements in generation quality over state-of-the-art baselines, accelerates inference by 10×, and—crucially—enables the first high-fidelity, controllable generation of large-scale structural properties.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Natural Language Processing: Generation

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Web Mining and Content Analysis: Bridging structured and unstructured data

Abstract

Given a set of graphs from some unknown family, we want to generate new graphs from that family. Recent methods use diffusion on either graph embeddings or the discrete space of nodes and edges. However, simple changes to embeddings (say, adding noise) can mean uninterpretable changes in the graph. In discrete-space diffusion, each step may add or remove many nodes/edges. It is hard to predict what graph patterns we will observe after many diffusion steps. Our proposed method, called GraphWeave, takes a different approach. We separate pattern generation and graph construction. To find patterns in the training graphs, we see how they transform vectors during random walks. We then generate new graphs in two steps. First, we generate realistic random walk "trajectories" which match the learned patterns. Then, we find the optimal graph that fits these trajectories. The optimization infers all edges jointly, which improves robustness to errors. On four simulated and five real-world benchmark datasets, GraphWeave outperforms existing methods. The most significant differences are on large-scale graph structures such as PageRank, cuts, communities, degree distributions, and flows. GraphWeave is also 10x faster than its closest competitor. Finally, GraphWeave is simple, needing only a transformer and standard optimizers.

Problem

• Generating new graphs from unknown graph families robustly
• Overcoming uninterpretable changes from embedding or discrete diffusion
• Separating pattern generation from graph construction for interpretability

Innovation

• Separates pattern generation from graph construction
• Generates realistic random walk trajectories first
• Infers optimal graph jointly from trajectories