On the properties of optimal weak links in consensus networks

Makan Fardad, Xi Zhang, Fu Lin, Mihailo R. Jovanovic

Research output: Contribution to journalConference articlepeer-review

5 Scopus citations


We study consensus networks in which each node updates its state by taking a weighted average of the states of its neighbors. Our objective is to determine the optimal set of weak links whose addition to the network maximally improves the efficiency of reaching consensus. Allocating a small amount of resources to the entire network with which new links can be created, we employ a perturbation method to cast this problem as a linear program. We demonstrate that the set of optimal weak links is sparse and, based on extensive numerical experiments, conjecture that they are also long-range. Examples are provided to illustrate the utility of our developments.

Original languageEnglish (US)
Article number7039712
Pages (from-to)2124-2129
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
Issue numberFebruary
StatePublished - 2014
Event2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 - Los Angeles, United States
Duration: Dec 15 2014Dec 17 2014


  • Convex optimization
  • linear programming
  • long-range links
  • opinion dynamics
  • perturbation analysis
  • social networks
  • sparsity


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