This article investigates the functional properties of complex networks used as grid computing systems. Complex networks following the Erdos-Renyi model and other models with a preferential attachment rule ( with and without growth) or priority to the connection of isolated nodes are studied. Regular networks are also considered for comparison. The processing load of the parallel program executed on the grid is assigned to the nodes on demand, and the efficiency of the overall computation is quantified in terms of the parallel speedup. It is found that networks with preferential attachment allow lower computing efficiency than networks with uniform link attachment. At the same time, considering only node clusters of the same size, preferential attachment networks display better efficiencies. The regular networks, on the other hand, display a poor efficiency, due to their implied larger internode distances. A correlation is observed between the topological properties of the network, specially average cluster size, and their respective computing efficiency.
