In this paper, we present an algorithm for finding the k highest-ranked (or Top-k) answers in a distributed network. A Top-K query returns the subset of most relevant answers, in place of all answers, for two reasons: (i) to minimize the cost metric that is associated with the retrieval of all answers; and (ii) to improve the recall and the precision of the answer-set, such that the user is not overwhelmed with irrelevant results. Our study focuses on multi-hop distributed networks in which the data is accessible by traversing a network of nodes. Such a setting captures very well the computation framework of emerging Sensor Networks, Peer-to-Peer Networks and Vehicular Networks. We present the Threshold Join Algorithm (TJA), an efficient algorithm that utilizes a non-uniform threshold on the queried attribute in order to minimize the transfer of data when a query is executed. Additionally, TJA resolves queries in the network rather than in a centralized fashion which further minimizes the consumption of bandwidth and delay. We performed an extensive experimental evaluation of our algorithm using a real testbed of 75 workstations along with a trace-driven experimental methodology. Our results indicate that TJA requires an order of magnitude less communication than the state-of-the-art, scales well with respect to the parameter k and the network topology.