Describing the Information Spreading on a Small-world Network Based on State Space

The investigation about the information spreading in a network has been described by the ODE dynamic system excellently. It has given a direct explanation to the statistic tendency on result. However it doesn't give enough information about the individual state. The investigation on the topology of a network can helpful to deal with the problem. The paper build a linear algebra model, which give a relationship between the ODE function groups and the graph topology. The model also give the distribution of the information in a network at the time of t. It is also satisfied with ODE in terms of statistical trendency.