The social media craze is on an ever increasing spree, and people are connected with each other like never before, but these vast connections are visually unexplored. We propose a methodology Twigraph to explore the connections between persons using their Twitter profiles. First, we propose a hybrid approach of recommending social media profiles, articles, and advertisements to a user.The profiles are recommended based on the similarity score between the user profile, and profile under evaluation. The similarity between a set of profiles is investigated by finding the top influential words thus causing a high similarity through an Influence Term Metric for each word. Then, we group profiles of various domains such as politics, sports, and entertainment based on the similarity score through a novel clustering algorithm. The connectivity between profiles is envisaged using word graphs that help in finding the words that connect a set of profiles and the profiles that are connected to a word. Finally, we analyze the top influential words over a set of profiles through clustering by finding the similarity of that profiles enabling to break down a Twitter profile with a lot of followers to fine level word connections using word graphs. The proposed method was implemented on datasets comprising 1.1 M Tweets obtained from Twitter. Experimental results show that the resultant influential words were highly representative of the relationship between two profiles or a set of profiles