In this book, we considered the issue of determination of the most effective user in the twitter online social network. We worked on a social network graph which have relationships (edges) between users who posted a tweet and other users who re-posted it. In other words, we assume that there is a relationship between User- X and User-Y when User-X posted a tweet and User-Y re-posted it. In Social Network Analysis (SNA), there are four fundamental centrality measures such as Degree Centrality, Closeness Centrality, Betweenness Centrality, and Eigenvector Centralities. We developed a new approach for determining the most effective user in Twitter online social network by using an index which named E-User (Effective User) Index. Through this index, we think that we are able to obtain more realistic results in SNA for Twitter. We designed a small weighted and directed social network graph by using a simulated data and used it for determining the most effective user in this study.