**
Enrico Lovisari**
University of Padova

We give an overview on both classical and recent results on two
performance metrics used to evaluate a linear consensus algorithm,
namely the rate of convergence of the network to its final value and
the l_{2}
norm of the discrepancy between the state and the final value.
The main goal is to analyze such metrics for families of increasing
graphs, showing the dependence on the number of agents in the network.
We illustrate results for graphs with symmetries (Cayley graphs) as well
as novel results on a class of geometric graphs. We also underline the
range of theoretical tools used in the proofs, which vary from geometric
characterization of the spectrum of a graph to state aggregation
techniques and electrical analogy between Markov Chains and resistive
networks.

Calendar of seminars