Construction of the network topology is the important premise and basis of the network simulation. Most of the complex network topology are constructed on the basis of random graph network. In this paper, we first simulate the random graph network by using Matlab software. But the random graph network maybe is disconnected, so we create an algorithm to construct a connected local network by using Prim algorithm to create a minimum spanning tree, and do the simulation by Matlab software. Finally we analyze the reliability of the constructed local network.
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