# Joint Network Topology Inference via a Shared Graphon Model

arXiv: https://arxiv.org/abs/2209.08223 · HTML: https://mlsanity.com/paper/2209.08223/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 90 references that are in the map.
- First posted on arXiv 17 Sep 2022.

## Builds on (most cited first, 30 of 30)

- [How to learn a graph from smooth signals](https://mlsanity.com/paper/1601.02513/) (2016)
- [Learning graphs from data: A signal representation perspective](https://mlsanity.com/paper/1806.00848/) (2018)
- [Connecting the Dots: Identifying Network Structure via Graph Signal Processing](https://mlsanity.com/paper/1810.13066/) (2018)
- [Global Convergence of ADMM in Nonconvex Nonsmooth Optimization](https://mlsanity.com/paper/1511.06324/) (2015)
- [Network Topology Inference from Spectral Templates](https://mlsanity.com/paper/1608.03008/) (2016)
- [Network Inference via the Time-Varying Graphical Lasso](https://mlsanity.com/paper/1703.01958/) (2017)
- [Stochastic blockmodel approximation of a graphon: Theory and consistent estimation](https://mlsanity.com/paper/1311.1731/) (2013)
- [Inference for multiple heterogeneous networks with a common invariant subspace](https://mlsanity.com/paper/1906.10026/) (2019)
- [A Consistent Histogram Estimator for Exchangeable Graph Models](https://mlsanity.com/paper/1402.1888/) (2014)
- [Learning Graphons via Structured Gromov-Wasserstein Barycenters](https://mlsanity.com/paper/2012.05644/) (2020)
- [Stationary Graph Processes and Spectral Estimation](https://mlsanity.com/paper/1603.04667/) (2016)
- [Estimating network edge probabilities by neighborhood smoothing](https://mlsanity.com/paper/1509.08588/) (2015)
- [Node-Based Learning of Multiple Gaussian Graphical Models](https://mlsanity.com/paper/1303.5145/) (2013)
- [Network histograms and universality of blockmodel approximation](https://mlsanity.com/paper/1312.5306/) (2013)
- [Joint Inference of Multiple Graphs from Matrix Polynomials](https://mlsanity.com/paper/2010.08120/) (2020)
- [Centrality measures for graphons: Accounting for uncertainty in networks](https://mlsanity.com/paper/1707.09350/) (2017)
- [High-Dimensional Joint Estimation of Multiple Directed Gaussian Graphical Models](https://mlsanity.com/paper/1804.00778/) (2018)
- [Network Topology Inference with Graphon Spectral Penalties](https://mlsanity.com/paper/2010.07872/) (2020)
- [Simultaneous Clustering and Estimation of Heterogeneous Graphical Models](https://mlsanity.com/paper/1611.09391/) (2016)
- [Joint Gaussian Graphical Model Estimation: A Survey](https://mlsanity.com/paper/2110.10281/) (2021)
- [Graph Laplacian mixture model](https://mlsanity.com/paper/1810.10053/) (2018)
- [Regularized Estimation of Piecewise Constant Gaussian Graphical Models: The Group-Fused Graphical Lasso](https://mlsanity.com/paper/1512.06171/) (2015)
- [EM-Based Smooth Graphon Estimation Using Bayesian and Spline-Based Approaches](https://mlsanity.com/paper/1903.06936/) (2019)
- [Joint inference of multiple graphs with hidden variables from stationary graph signals](https://mlsanity.com/paper/2110.03666/) (2021)
- [Change-point detection in dynamic networks via graphon estimation](https://mlsanity.com/paper/1908.01823/) (2019)
- [Efficient Variational Bayes Learning of Graphical Models with Smooth Structural Changes](https://mlsanity.com/paper/2009.07703/) (2020)
- [Variational Bayes model averaging for graphon functions and motif frequencies inference in W-graph models](https://mlsanity.com/paper/1310.6150/) (2013)
- [rags2ridges: A One-Stop-Shop for Graphical Modeling of High-Dimensional Precision Matrices](https://mlsanity.com/paper/2010.05619/) (2020)
- [Modularity maximisation for graphons](https://mlsanity.com/paper/2101.00503/) (2021)
- [Graphon-aided Joint Estimation of Multiple Graphs](https://mlsanity.com/paper/2202.05686/) (2022)

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

- [Scalable Implicit Graphon Learning](https://mlsanity.com/paper/2410.17464/) (2024)
- [Recovering Missing Node Features with Local Structure-based Embeddings](https://mlsanity.com/paper/2309.09068/) (2023)
- [Joint graph learning from Gaussian observations in the presence of hidden nodes](https://mlsanity.com/paper/2212.01816/) (2022)
- [Multiview Graph Learning with Consensus Graph](https://mlsanity.com/paper/2401.13769/) (2024)
- [A Few Moments Please: Scalable Graphon Learning via Moment Matching](https://mlsanity.com/paper/2506.04206/) (2025)
- [Online Network Inference from Graph-Stationary Signals with Hidden Nodes](https://mlsanity.com/paper/2409.08760/) (2024)
- [Enhancing Graphical Lasso: A Robust Scheme for Non-Stationary Mean Data](https://mlsanity.com/paper/2503.19651/) (2025)
- [Model-Driven Graph Contrastive Learning](https://mlsanity.com/paper/2506.06212/) (2025)
- [From Moments to Models: Graphon-Mixture Learning for Mixup and Contrastive Learning](https://mlsanity.com/paper/2510.03690/) (2025)
- [Co-Hub Node Based Multiview Graph Learning with Theoretical Guarantees](https://mlsanity.com/paper/2512.12435/) (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 estimating the topology of multiple networks from nodal observations, where these networks are assumed to be drawn from the same (unknown) random graph model. We adopt a graphon as our random graph model, which is a nonparametric model from which graphs of potentially different sizes can be drawn. The versatility of graphons allows us to tackle the joint inference problem even for the cases where the graphs to be recovered contain different number of nodes and lack precise alignment across the graphs. Our solution is based on combining a maximum likelihood penalty with graphon estimation schemes and can be used to augment existing network inference methods. The proposed joint network and graphon estimation is further enhanced with the introduction of a robust method for noisy graph sampling information. We validate our proposed approach by comparing its performance against competing methods in synthetic and real-world datasets.