# Connecting the Dots: Identifying Network Structure via Graph Signal Processing

arXiv: https://arxiv.org/abs/1810.13066 · HTML: https://mlsanity.com/paper/1810.13066/

## Key facts

- Cited by 111 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Oct 2018.

## Built on by (most cited first, 30 of 111)

- [FourierGNN: Rethinking Multivariate Time Series Forecasting from a Pure Graph Perspective](https://mlsanity.com/paper/2311.06190/) (2023)
- [Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyond](https://mlsanity.com/paper/2101.05510/) (2021)
- [FreDF: Learning to Forecast in the Frequency Domain](https://mlsanity.com/paper/2402.02399/) (2024)
- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Time-o1: Time-Series Forecasting Needs Transformed Label Alignment](https://mlsanity.com/paper/2505.17847/) (2025)
- [Learning Parametrised Graph Shift Operators](https://mlsanity.com/paper/2101.10050/) (2021)
- [Accelerated Graph Learning from Smooth Signals](https://mlsanity.com/paper/2110.09677/) (2021)
- [Synthesizing Decentralized Controllers with Graph Neural Networks and Imitation Learning](https://mlsanity.com/paper/2012.14906/) (2020)
- [Learning Time-Varying Graphs from Online Data](https://mlsanity.com/paper/2110.11017/) (2021)
- [Joint Network Topology Inference via a Shared Graphon Model](https://mlsanity.com/paper/2209.08223/) (2022)
- [Fair GLASSO: Estimating Fair Graphical Models with Unbiased Statistical Behavior](https://mlsanity.com/paper/2406.09513/) (2024)
- [Quadratic Direct Forecast for Training Multi-Step Time-Series Forecast Models](https://mlsanity.com/paper/2511.00053/) (2025)
- [Learning Hypergraphs From Signals With Dual Smoothness Prior](https://mlsanity.com/paper/2211.01717/) (2022)
- [Frequency Spectrum is More Effective for Multimodal Representation and Fusion: A Multimodal Spectrum Rumor Detector](https://mlsanity.com/paper/2312.11023/) (2023)
- [Online Graph Learning under Smoothness Priors](https://mlsanity.com/paper/2103.03762/) (2021)
- [Learning to Infer Structures of Network Games](https://mlsanity.com/paper/2206.08119/) (2022)
- [Fairness-Aware Graph Filter Design](https://mlsanity.com/paper/2303.11459/) (2023)
- [Polynomial Graphical Lasso: Learning Edges from Gaussian Graph-Stationary Signals](https://mlsanity.com/paper/2404.02621/) (2024)
- [Beyond the Federation: Topology-aware Federated Learning for Generalization to Unseen Clients](https://mlsanity.com/paper/2407.04949/) (2024)
- [Non-negative Weighted DAG Structure Learning](https://mlsanity.com/paper/2409.07880/) (2024)
- [A Computational Framework for Modeling Complex Sensor Network Data Using Graph Signal Processing and Graph Neural Networks in Structural Health Monitoring](https://mlsanity.com/paper/2105.05316/) (2021)
- [Bures-Wasserstein Means of Graphs](https://mlsanity.com/paper/2305.19738/) (2023)
- [Joint inference of multiple graphs with hidden variables from stationary graph signals](https://mlsanity.com/paper/2110.03666/) (2021)
- [Learning Graph Structure from Convolutional Mixtures](https://mlsanity.com/paper/2205.09575/) (2022)
- [Learning Product Graphs from Spectral Templates](https://mlsanity.com/paper/2211.02893/) (2022)
- [Distributionally Robust Graph Learning from Smooth Signals under Moment Uncertainty](https://mlsanity.com/paper/2105.05458/) (2021)
- [Laplacian Constrained Precision Matrix Estimation: Existence and High Dimensional Consistency](https://mlsanity.com/paper/2111.00590/) (2021)
- [Learning Sparse Graphs via Majorization-Minimization for Smooth Node Signals](https://mlsanity.com/paper/2202.02815/) (2022)
- [Learning Expanding Graphs for Signal Interpolation](https://mlsanity.com/paper/2203.07966/) (2022)
- [An Unbiased Symmetric Matrix Estimator for Topology Inference under Partial Observability](https://mlsanity.com/paper/2203.15500/) (2022)

## Abstract (arXiv)

Network topology inference is a prominent problem in Network Science. Most graph signal processing (GSP) efforts to date assume that the underlying network is known, and then analyze how the graph's algebraic and spectral characteristics impact the properties of the graph signals of interest. Such an assumption is often untenable beyond applications dealing with e.g., directly observable social and infrastructure networks; and typically adopted graph construction schemes are largely informal, distinctly lacking an element of validation. This tutorial offers an overview of graph learning methods developed to bridge the aforementioned gap, by using information available from graph signals to infer the underlying graph topology. Fairly mature statistical approaches are surveyed first, where correlation analysis takes center stage along with its connections to covariance selection and high-dimensional regression for learning Gaussian graphical models. Recent GSP-based network inference frameworks are also described, which postulate that the network exists as a latent underlying structure, and that observations are generated as a result of a network process defined in such a graph. A number of arguably more nascent topics are also briefly outlined, including inference of dynamic networks, nonlinear models of pairwise interaction, as well as extensions to directed graphs and their relation to causal inference. All in all, this paper introduces readers to challenges and opportunities for signal processing research in emerging topic areas at the crossroads of modeling, prediction, and control of complex behavior arising in networked systems that evolve over time.