On the properties of optimal weak links in consensus networks

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

Research output: Contribution to journalArticlepeer-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
JournalUnknown Journal
Issue numberFebruary
StatePublished - 2014


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

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization


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