Consensus-Based Distributed Computation of Link-Based Network Metrics

Average consensus algorithms have wide applications in distributed computing systems where all the nodes agree on the average value of their initial states by only exchanging information with their local neighbors. In this letter, we look into link-based network metrics which are polynomial functions of pair-wise node attributes defined over the links in a network. Different from node-based average consensus, such link-based metrics depend on both the distribution of node attributes and the underlying network topology. We propose a general algorithm using the weighted average consensus protocol for the distributed computation of link-based network metrics and provide the convergence conditions and convergence rate analysis.