We analyze a distributed information network in which each node has access to the information contained in a limited set of nodes (its neighborhood) at a given time. A collective computation is carried out in which each node calculates a value that implies all information contained in the network (in our case, the average value of a variable that can take different values in each network node). The neighborhoods can change dynamically by exchanging neighbors with other nodes. The results of this collective calculation show rapid convergence and good scalability with the network size. These results are compared with those of a fixed network arranged as a square lattice, in which the number of rounds to achieve a given accuracy is very high when the size of the network increases. The results for the evolving networks are interpreted in light of the properties of complex networks and are directly relevant to the diameter and characteristic path length of the networks, which seem to express "small world" properties.