In today’s world, most of us use social media regularly. The prevalence of Social Media is increasing day by day. The most used online social networking (OSN) platforms are Facebook, Instagram, Twitter, WhatsApp. Graph Theory, in mathematics is known for its many applications in real life. One such is modelling social structures based on different kinds of relationships between people or groups of people. As the new age social relationships of groups of people reflect in the social networking media that are extensively used, Facebook, Instagram, Twitter and WhatsApp can be modelled using Graphs. Facebook, in itself owns both WhatsApp and Instagram. The massive success of Facebook is amusing to most competitors in the business. In this paper, it is discussed, through concepts of Graph Theory how the interconnection between different social media owned by Facebook works and it is tried to explain the success of Facebook.