Markov过程对一类改进BA模型度分布的分析

Analysis of the Markov process for degree distribution of an improved model BA

提出对原始的BA模型进行修正,使得模型中原始节点的度分布都不为0,同时每个原始节点被连接的概率都不为0.改进了复杂网络度分布概率的统计定义,将原始节点和时间概念都考虑在内,使度分布的定义更加符合实际.用Markov过程对修改的BA模型度分布进行分析,得出能描述度分布随度值和时间演化的矩阵方程,并做出模型的度分布对数关系的数值模拟图.

The original model BA was modified so that the degree distribution of its original node was not zero, while the connective probability of each original node was not zero. The statistical definition of degree distribution probability of complex networks was thus improved. The original node and time were taken into account so that the concept of the definition of degree distribution became more realistic. The degree distribution of modified model BA was analyzed by the Markov process; then the matrix equation was obtained which can describes the degree distribution with the degree of value and the time evolution. Lastly the numerical simulation chart of the degree distribution of logarithmic relations was compiled.