Statistical physics of social networking

In this work we make an attempt to understand social networks from a mathematical viewpoint. In the first instance we consider a network where each node representing an individual can connect with a neighbouring node with a certain probability along with connecting with individuals who are friends of friends. We find that above a particular value of a chosen combination of parameters, the probability of connection between two widely separated nodes is a scale free. We next consider a simplified case of online social media networks in which each individual adds at a friends at constant probability per unit time: friends from a suggested neighbourhood as well as from his/her friendlist. We find that in the limit of large times since formation of the network, the probability of connection between two widely separated individuals is a scale free quantity. We hence, demonstrate a different scale free facet of networks not discussed before in literature.