Minimal sets to destroy the k-core in random networks.

Journal Article (Journal Article)

We study the problem of finding the smallest set of nodes in a network whose removal results in an empty k-core, where the k-core is the subnetwork obtained after the iterative removal of all nodes of degree smaller than k. This problem is also known in the literature as finding the minimal contagious set. The main contribution of our work is an analysis of the performance of the recently introduced corehd algorithm [Zdeborová, Zhang, and Zhou, Sci. Rep. 6, 37954 (2016)10.1038/srep37954] on random graphs taken from the configuration model via a set of deterministic differential equations. Our analyses provide upper bounds on the size of the minimal contagious set that improve over previously known bounds. Our second contribution is a heuristic called the weak-neighbor algorithm that outperforms all currently known local methods in the regimes considered.

Full Text

Duke Authors

Cited Authors

  • Schmidt, C; Pfister, HD; Zdeborová, L

Published Date

  • February 2019

Published In

Volume / Issue

  • 99 / 2-1

Start / End Page

  • 022310 -

PubMed ID

  • 30934241

Electronic International Standard Serial Number (EISSN)

  • 2470-0053

International Standard Serial Number (ISSN)

  • 2470-0045

Digital Object Identifier (DOI)

  • 10.1103/physreve.99.022310


  • eng