# Diffusion Source Identification on Networks with Statistical Confidence

arXiv: https://arxiv.org/abs/2106.04800 · HTML: https://mlsanity.com/paper/2106.04800/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 31 references that are in the map.
- First posted on arXiv 9 Jun 2021.

## Builds on (most cited first, 7 of 7)

- [Stacking Models for Nearly Optimal Link Prediction in Complex Networks](https://mlsanity.com/paper/1909.07578/) (2019)
- [Finding Adam in random growing trees](https://mlsanity.com/paper/1411.3317/) (2014)
- [Rooting out the Rumor Culprit from Suspects](https://mlsanity.com/paper/1301.6312/) (2013)
- [Confidence Sets for the Source of a Diffusion in Regular Trees](https://mlsanity.com/paper/1510.05461/) (2015)
- [Informative core identification in complex networks](https://mlsanity.com/paper/2101.06388/) (2021)
- [Approximate Identification of the Optimal Epidemic Source in Complex Networks](https://mlsanity.com/paper/1906.03052/) (2019)
- [Multiple Infection Sources Identification with Provable Guarantees](https://mlsanity.com/paper/1608.06492/) (2016)

## Built on by (most cited first, 5 of 5)

- [Reconstructing Graph Diffusion History from a Single Snapshot](https://mlsanity.com/paper/2306.00488/) (2023)
- [Social-Inverse: Inverse Decision-making of Social Contagion Management with Task Migrations](https://mlsanity.com/paper/2209.10493/) (2022)
- [Learning the Topology and Behavior of Discrete Dynamical Systems](https://mlsanity.com/paper/2402.11686/) (2024)
- [Efficient PAC Learnability of Dynamical Systems Over Multilayer Networks](https://mlsanity.com/paper/2405.06884/) (2024)
- [Conformal Prediction for Multi-Source Detection on a Network](https://mlsanity.com/paper/2511.08867/) (2025)

## Abstract (arXiv)

Diffusion source identification on networks is a problem of fundamental importance in a broad class of applications, including rumor controlling and virus identification. Though this problem has received significant recent attention, most studies have focused only on very restrictive settings and lack theoretical guarantees for more realistic networks. We introduce a statistical framework for the study of diffusion source identification and develop a confidence set inference approach inspired by hypothesis testing. Our method efficiently produces a small subset of nodes, which provably covers the source node with any pre-specified confidence level without restrictive assumptions on network structures. Moreover, we propose multiple Monte Carlo strategies for the inference procedure based on network topology and the probabilistic properties that significantly improve the scalability. To our knowledge, this is the first diffusion source identification method with a practically useful theoretical guarantee on general networks. We demonstrate our approach via extensive synthetic experiments on well-known random network models and a mobility network between cities concerning the COVID-19 spreading.