Open Access
2022 Shotgun assembly of Erdős-Rényi random graphs
Julia Gaudio, Elchanan Mossel
Author Affiliations +
Electron. Commun. Probab. 27: 1-14 (2022). DOI: 10.1214/22-ECP445


Graph shotgun assembly refers to the problem of reconstructing a graph from a collection of local neighborhoods. In this paper, we consider shotgun assembly of Erdős–Rényi random graphs G(n,pn), where pn=nα for 0<α<1. We consider both reconstruction up to isomorphism as well as exact reconstruction (recovering the vertex labels as well as the structure). We show that given the collection of distance-1 neighborhoods, G is exactly reconstructable for 0<α<13, but not reconstructable for 12<α<1. Given the collection of distance-2 neighborhoods, G is exactly reconstructable for α0,1212,35, but not reconstructable for 34<α<1.

Funding Statement

E.M is partially supported by Vannevar Bush Faculty Fellowship ONR-N00014-20-1-2826, NSF awards CCF 1918421 and DMS-1737944, ARO MURI grant W911NF1910217 and by a Simons Investigator award.


We thank the anonymous reviewer for a very careful review. The reviewer’s comments caught several errors, and improved the clarity and presentation of this work.


Download Citation

Julia Gaudio. Elchanan Mossel. "Shotgun assembly of Erdős-Rényi random graphs." Electron. Commun. Probab. 27 1 - 14, 2022.


Received: 13 January 2021; Accepted: 5 January 2022; Published: 2022
First available in Project Euclid: 19 January 2022

MathSciNet: MR4375912
Digital Object Identifier: 10.1214/22-ECP445

Primary: 05C80

Keywords: Random graphs , shotgun assembly

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