Recently, on-line social network has been increasing according to development of internet. The most representative service is blog. A Blog is a type of personal web site, usually maintained by an individual with regular entries of commentary. These blogs are related to each other, and it is called Blog Network in this paper. In a blog network, posts in a blog can be diffused to other blogs. Analyzing information diffusion in a blog world is a very useful research issue, which can be used for predicting information diffusion, abnormally detection, marketing, and revitalizing the blog world. Existing studies on network analysis have no consideration for the passage of time and these approaches can only measure network activity for a node by the number of direct connections that a given node has. As one solution, this paper suggests the new method of measuring the blog network activity using logistic curve model and Cosine-similarity in key words by the Map/Reduce programming model.