Weighted Random Dot Product Graphs: Extending Network Models to Handle Heterogeneous Edge Weights
A new statistical model called the Weighted Random Dot Product Graph (WRDPG) has been published in the Electronic Journal of Statistics, extending the classical RDPG framework to graphs where edges carry heterogeneous weights. Unlike prior approaches, the model uses moment-generating functions to distinguish between weight distributions that share the same mean but differ in higher-order moments. This advance broadens the toolkit available for analyzing complex relational data in network science and machine learning.
The paper, authored by Bernardo Marenco and colleagues and published in the Electronic Journal of Statistics (2026), introduces a nonparametric Weighted Random Dot Product Graph (WRDPG) model that assigns sequences of latent positions to each node in a network. Inner products of these nodal vectors encode the moments of edge-weight distributions through moment-generating functions, enabling the model to differentiate distributions with identical means but differing higher-order moments—a limitation of prior art. The authors adapt the adjacency spectral embedding estimator to this weighted setting and establish formal statistical guarantees, including consistency and asymptotic normality. They also develop a generative framework that allows researchers to sample synthetic graphs conforming to a prescribed or data-fitted WRDPG, supporting hypothesis testing and benchmarking of observed graph metrics. The paper includes 12 figures and reproducible code examples demonstrating the model's effectiveness across a range of network analytic applications.
What's missing
The paper does not discuss computational scalability of the proposed spectral embedding estimator for very large graphs, nor does it address how the model performs when edge-weight distributions are heavy-tailed or exhibit extreme outliers.
What different sources said
- arXiv cs.LGCenter
Weighted Random Dot Product Graphs
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