Translator Disclaimer
February 2023 The diameter of the directed configuration model
Xing Shi Cai, Guillem Perarnau
Author Affiliations +
Ann. Inst. H. Poincaré Probab. Statist. 59(1): 244-270 (February 2023). DOI: 10.1214/22-AIHP1252


We show that the diameter of the directed configuration model with n vertices rescaled by logn converges in probability to a constant. Our assumptions are the convergence of the in- and out-degree of a uniform random vertex in distribution, first and second moment. Our result extends previous results on the diameter of the model and applies to many other random directed graphs.

Nous montrons que le diamètre du modèle de configuration dirigé avec n sommets renormalisé par logn converge en probabilité vers une constante. Nos hypothèses sont la convergence en loi des degrés entrant et sortant d’un sommet uniformément choisi, et celles en moments d’ordre 1 et d’ordre 2. Notre résultat étend les résultats précédents sur le diamètre du modèle et s’applique à de nombreux autres graphes orientés aléatoires.

Funding Statement

This work is supported by the Agencia Estatal de Investigación (MCIN/AEI) through the a Proyecto I+D+i 2020 (PID2020-113082GB-I00), through the Marie Skłodowska-Curie Research and Innovation Staff Exchange grant RandNet (MSCA-RISE-2020-101007705) and through the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D (CEX2020-001084-M).


We thank Svante Janson for helpful discussions on branching processes in the subcritical regime.


Download Citation

Xing Shi Cai. Guillem Perarnau. "The diameter of the directed configuration model." Ann. Inst. H. Poincaré Probab. Statist. 59 (1) 244 - 270, February 2023.


Received: 11 March 2020; Revised: 28 April 2021; Accepted: 4 February 2022; Published: February 2023
First available in Project Euclid: 16 January 2023

Digital Object Identifier: 10.1214/22-AIHP1252

Primary: 05C80 , 60C05

Keywords: diameter , directed configuration model , distances

Rights: Copyright © 2023 Association des Publications de l’Institut Henri Poincaré


This article is only available to subscribers.
It is not available for individual sale.

Vol.59 • No. 1 • February 2023
Back to Top