During an intercommunication period in social network participants either upgrade the interest in a topic through their positive inputs, catchy comments, tag lines or they simply do not show any interest. The activity of the participants motive for refinement in the topic state after a certain period of time. Moreover, the scenario of interaction could be leverage as an imprecise and non-crisp scheme. So the process is all about to know the transition state of a topic over a certain period of time. There are huge amount of data available in the random social networks such as facebook, twitter etc., In these data from the conversation block is used to place the topic in concern category. These topics categorization is fully based upon FA(Firefly Algorithm) using Matlab. The firefly Algorithm gathers the data on social network and based on the information it groups the data those are all having the similar attributes.