  This paper focuses on non-asymptotic diffusion time in asynchronous gossip
protocols. Asynchronous gossip protocols are designed to perform distributed
computation in a network of nodes by randomly exchanging messages on the
associated graph. To achieve consensus among nodes, a minimal number of
messages has to be exchanged. We provides a probabilistic bound to such number
for the general case. We provide a explicit formula for fully connected graphs
depending only on the number of nodes and an approximation for any graph
depending on the spectrum of the graph.
