Departmental Papers (ESE)


In this paper, we consider a consensus seeking process based on repeated averaging in a randomly changing network. The underlying graph of such a network at each time is generated by a martingale random process. We prove that consensus is reached almost surely if and only if the expected graph of the network contains a directed spanning tree. We then provide an example of a consensus seeking process based on local averaging of opinions in a dynamic model of social network formation which is a martingale. At each time step, individual agents randomly choose some other agents to interact with according to some arbitrary probabilities. The interaction is one-sided and results in the agent averaging her opinion with those of her randomly chosen neighbors based on the weights she assigns to them. Once an agent chooses a neighbor, the weights are updated in such a way that the expected values of the weights are preserved. We show that agents reach consensus in this random dynamical network almost surely. Finally, we demonstrate that a Polya Urn process is a martingale process, and our prior results in [1] is a special case of the model proposed in this paper.

Document Type

Conference Paper

Subject Area


Date of this Version



Fazeli, A. & Jadbabaie, A. (2012). Consensus over martingale graph processes. American Control Conference (ACC), 2012, pp.845-850.

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Consensus, Stochastic Process, Social Networks, Random Networks, Graph Theory



Date Posted: 23 January 2013

This document has been peer reviewed.