The social network consists of a number of social entities and their conducted social interactions. In a social network, many social behaviors exhibit the property of association that the behaviors of an individual influence the others who are contacted. For example, the message that carries the news may spread through a portion of the social network that constructs a social interaction propagation graph. We advocate the interaction and influence to be studied by using network graphic theory and inferring models. We model the social interaction influence and its propagation over the social network. We then compute the infection probability in the social interaction propagation graph. Furthermore, we implement the Apriori algorithm that allows us to explore the social interaction association and compute the infection probability on a large scale social network. The complexity is compared with a centralized implementation and a distributed implementation.