  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.
