The mean short path of network is discussed. The mean short path of the network product is equal to the sum of the mean short path of the networks. Based on this we calculate the mean short path of several constructed networks.

With the development of massively parallel processing, it is necessary that the parallel applications would be capable of good scalability. It is described how to use the near optimal scalability analysis method with the two dimensional electromagnetic plasma parallel program using particle in cell method as an example. Having known the performance of small parallel systems, one can obtain the information about how many processors which the larger systems are running on can obtain the more"reasonable" performance when using the near optimal scalability analysis. A suit of practical scalability evaluation method is also proposed to find the reason why the practical scalability is bad, and help to optimize the application programs.

In view of the special needs for systems of difference equations of 2-D heat conduction coupled three temperature,the block G-S algorithm and the ICCG algorithm are presented and compared.Numerical results show that the ICCG algorithm is thousands times faster than the block G-S algorithm.Furthermore,in 2-D numerical simulation of laser hohlraum target coupling,the ICCG algorithm will raise greatly computational efficiency if it can realize vectorzation operation.