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This article investigated the statistical characteristics of complex networks, and provided theoretical guidance to the construction of a grid computing systems. Complex networks following the ER model and other models with a preferential attachment rule (with or without growth) were studied. The emphasis was placed on the investigation of networks with growth. In complex grid computing systems, the processing load of the parallel program executed on the grid was assigned to the nodes on demand by the master node, and the efficiency of the overall computation was quantified in terms of the parallel speedup. It was found that networks with growth have better parallel efficiency and the performance of nodes more regular. An interesting thing found by simulation was that in networks with growth there existed a core sub-graph, and the origin node took the core of the whole network. The results got from this paper were valuable for the construction of Grid with high efficiency.