  This article investigates the performance of grid computing systems whose
interconnections are given by random and scale-free complex network models.
Regular networks, which are common in parallel computing architectures, are
also used as a standard for comparison. The processing load is assigned to the
processing nodes on demand, and the efficiency of the overall computing is
quantified in terms of the respective speed-ups. It is found that random
networks allow higher computing efficiency than their scale-free counterparts
as a consequence of the smaller number of isolated clusters implied by the
former model. At the same time, for fixed cluster sizes, the scale free model
tend to provide slightly better efficiency. Two modifications of the random and
scale free paradigms, where new connections tend to favor more recently added
nodes, are proposed and shown to be more effective for grid computing than the
standard models. A well-defined correlation is observed between the topological
properties of the network and their respective computing efficiency.
