Twitter serves as a data source for many Natural Language Processing (NLP) tasks. It can be challenging to identify topics on Twitter due to continuous updating data stream. In this paper, we present an unsupervised graph based framework to identify the evolution of sub-topics within two weeks of real-world Twitter data. We first employ a Markov Clustering Algorithm (MCL) with a node removal method to identify optimal graph clusters from temporal Graph-of-Words (GoW). Subsequently, we model the clustering transitions between the temporal graphs to identify the topic evolution. Finally, the transition flows generated from both computational approach and human annotations are compared to ensure the validity of our framework.