In bioinformatics research area, many scholars from physiology, physics, mahtematics, computer science and other discliplines probe in the profound of genetic engineering via integrating expermential researchers and theoretical analysis, and try exposes the nature of biological genetic information. We investigate connections between power law degree distribution and cumulative degree distributions of scale-free network models. First, we enumerate several classical deterministic network models with scale-free topological structure and analysis the connections between degree distribution and cumulative degree distributions. Second, we apply the random network models to state the connection between power law degree distribution and cumulative degree distributions. Finally, as a further research step, we probe the reasons that make the gaps between them.