Consensus over ergodic stationary graph processes

Alireza Tahbaz-Salehi*, Ali Jadbabaie

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

192 Scopus citations


In this technical note, we provide a necessary and sufficient condition for convergence of consensus algorithms when the underlying graphs of the network are generated by an ergodic and stationary random process. We prove that consensus algorithms converge almost surely, if and only if, the expected graph of the network contains a directed spanning tree. Our results contain the case of independent and identically distributed graph processes as a special case. We also compute the mean and variance of the random consensus value that the algorithm converges to and provide a necessary and sufficient condition for the distribution of the consensus value to be degenerate.

Original languageEnglish (US)
Article number5340530
Pages (from-to)225-230
Number of pages6
JournalIEEE Transactions on Automatic Control
Issue number1
StatePublished - Jan 2010


  • Consensus algorithm
  • Ergodic stationary process
  • Random graph

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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