In this letter, we present an eavesdropping-based gossip algorithm (EBGA). In the novel algorithm, when a node unicasts its values to a randomly selected neighboring node, all other nodes, which eavesdrop these values, simultaneously update their state values. By exploiting the broadcast nature of wireless communications, this novel algorithm has similar performance to broadcast gossip algorithms.
Although broadcast gossip algorithms have the fastest rate of convergence among all gossip algorithms, they either converge to a random value rather than the average consensus, or need out-degree information available for each node to guarantee convergence to the average consensus. Utilizing non-negative matrix theory and ergodicity coefficient, we have proved that this novel algorithm can converge to the average consensus without any assumption which is difficult to be realized in realnetworks.