Abstract: Industrial competition practices have shown that the third-party E-business platform has typical characteristics of networked market, in which the positive feedback mechanism leads to platform success provided that the number of platform users surpasses its critical mass. Otherwise, the platform would diminish and disappear in the market under the effect of the negative feedback mechanism. Therefore, it is very important to reveal the influence factors of the critical mass of platform users and explore its estimation method. This paper, apply the complex network method to develop a dynamical model to describe the number of platform users,which is varying with the time after the platform introduced into market. Based on the proposed platform diffusion model, the influence factors and mechanisms are analyzed. Results show that (1) the platform user network structure and the users' decision threshold value are the main factors to determine the critical mass of platform users (2) the heterogeneity of network structure (the standard deviation of degree distributions) is in roughly power function of the critical mass of platform users (3) the improvement degree of service quality in the new platform, the learning cost of users switching from the existing platform to the new platform, and the compatibility between the existing and the new platforms have strong influence on the critical mass of platform users through changing users' decision threshold value. Combining a sampling case, it has also been discussed how the companies apply the estimation method of platform critical mass in practice.

Key words: critical mass of users, E-Business platform, complex networks