# Weighted Random Dot Product Graphs

arXiv: https://arxiv.org/abs/2505.03649 · HTML: https://mlsanity.com/paper/2505.03649/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 43 references that are in the map.
- First posted on arXiv 6 May 2025.

## Builds on (most cited first, 12 of 12)

- [Statistical inference on random dot product graphs: a survey](https://mlsanity.com/paper/1709.05454/) (2017)
- [A statistical interpretation of spectral embedding: the generalised random dot product graph](https://mlsanity.com/paper/1709.05506/) (2017)
- [Moving Beyond Sub-Gaussianity in High-Dimensional Statistics: Applications in Covariance Estimation and Linear Regression](https://mlsanity.com/paper/1804.02605/) (2018)
- [Community Detection and Classification in Hierarchical Stochastic Blockmodels](https://mlsanity.com/paper/1503.02115/) (2015)
- [Sharp Concentration Results for Heavy-Tailed Distributions](https://mlsanity.com/paper/2003.13819/) (2020)
- [Bootstrapping Networks with Latent Space Structure](https://mlsanity.com/paper/1907.10821/) (2019)
- [Spectral embedding of weighted graphs](https://mlsanity.com/paper/1910.05534/) (2019)
- [Online Change Point Detection for Weighted and Directed Random Dot Product Graphs](https://mlsanity.com/paper/2201.11222/) (2022)
- [Robust Estimation from Multiple Graphs under Gross Error Contamination](https://mlsanity.com/paper/1707.03487/) (2017)
- [Connectome Smoothing via Low-rank Approximations](https://mlsanity.com/paper/1609.01672/) (2016)
- [A Random Dot Product Model for Weighted Networks](https://mlsanity.com/paper/1611.02530/) (2016)
- [Networks of international football: communities, evolution and globalization of the game](https://mlsanity.com/paper/2205.10599/) (2022)

## Built on by (most cited first, 1 of 1)

- [Subspace Projection Methods for Fast Spectral Embeddings of Evolving Graphs](https://mlsanity.com/paper/2603.19439/) (2026)

## Abstract (arXiv)

Modeling of intricate relational patterns has become a cornerstone of contemporary statistical research and related data science fields. Networks, represented as graphs, offer a natural framework for this analysis. This paper extends the Random Dot Product Graph (RDPG) model to accommodate weighted graphs, markedly broadening the model's scope to scenarios where edges exhibit heterogeneous weight distributions. We propose a nonparametric weighted (W)RDPG model that assigns a sequence of latent positions to each node. Inner products of these nodal vectors specify the moments of their incident edge weights' distribution via moment-generating functions. In this way, and unlike prior art, the WRDPG can discriminate between weight distributions that share the same mean but differ in other higher-order moments. We derive statistical guarantees for an estimator of the nodal's latent positions adapted from the workhorse adjacency spectral embedding, establishing its consistency and asymptotic normality. We also contribute a generative framework that enables sampling of graphs that adhere to a (prescribed or data-fitted) WRDPG, facilitating, e.g., the analysis and testing of observed graph metrics using judicious reference distributions. The paper is organized to formalize the model's definition, the estimation (or nodal embedding) process and its guarantees, as well as the methodologies for generating weighted graphs, all complemented by illustrative and reproducible examples showcasing the WRDPG's effectiveness in various network analytic applications.