# Network Topology Inference with Graphon Spectral Penalties

arXiv: https://arxiv.org/abs/2010.07872 · HTML: https://mlsanity.com/paper/2010.07872/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Oct 2020.

## Built on by (most cited first, 11 of 11)

- [Joint Network Topology Inference via a Shared Graphon Model](https://mlsanity.com/paper/2209.08223/) (2022)
- [Scalable Implicit Graphon Learning](https://mlsanity.com/paper/2410.17464/) (2024)
- [Non-negative Weighted DAG Structure Learning](https://mlsanity.com/paper/2409.07880/) (2024)
- [A Few Moments Please: Scalable Graphon Learning via Moment Matching](https://mlsanity.com/paper/2506.04206/) (2025)
- [Network Clustering for Latent State and Changepoint Detection](https://mlsanity.com/paper/2111.01273/) (2021)
- [Distributed Graph Learning with Smooth Data Priors](https://mlsanity.com/paper/2112.05887/) (2021)
- [Graphon-aided Joint Estimation of Multiple Graphs](https://mlsanity.com/paper/2202.05686/) (2022)
- [Temporal Attention Evolutional Graph Convolutional Network for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2505.00302/) (2025)
- [Model-Driven Graph Contrastive Learning](https://mlsanity.com/paper/2506.06212/) (2025)
- [Non-negative DAG Learning from Time-Series Data](https://mlsanity.com/paper/2512.07267/) (2025)
- [Feasible Flow Matching for Graph Reconstruction via Within-Sampling Primal-Dual Guidance](https://mlsanity.com/paper/2609.32980/) (2026)

## Abstract (arXiv)

We consider the problem of inferring the unobserved edges of a graph from data supported on its nodes. In line with existing approaches, we propose a convex program for recovering a graph Laplacian that is approximately diagonalizable by a set of eigenvectors obtained from the second-order moment of the observed data. Unlike existing work, we incorporate prior knowledge about the distribution from where the underlying graph was drawn. In particular, we consider the case where the graph was drawn from a graphon model, and we supplement our convex optimization problem with a provably-valid regularizer on the spectrum of the graph to be recovered. We present the cases where the graphon model is assumed to be known and the more practical setting where the relevant features of the model are inferred from auxiliary network observations. Numerical experiments on synthetic and real-world data illustrate the advantage of leveraging the proposed graphon prior, even when the prior is imperfect.