Title: A Viral Timeline Branching Process to study a Social Network,
Abstract: Bio-inspired paradigms are proving to be useful in analyzing propagation and
dissemination of information in networks. In this paper we explore the use of
multi-type branching processes to analyse viral properties of content in a
social network, with and without competition from other sources. We derive and
compute various virality measures, e.g., probability of virality, expected
number of shares, or the rate of growth of expected number of shares etc. They
allow one to predict the emergence of global macro properties (e.g., viral
spread of a post in the entire network) from the laws and parameters that
determine local interactions. The local interactions, greatly depend upon the
structure of the timelines holding the content and the number of friends (i.e.,
connections) of users of the network. We then formulate a non-cooperative game
problem and study the Nash equilibria as a function of the parameters. The
branching processes modelling the social network under competition turn out to
be decomposable, multi-type and continuous time variants. For such processes
types belonging to different sub-classes evolve at different rates and have
different probabilities of extinction etc. We compute content provider wise
extinction probability, rate of growth etc. We also conjecture the
content-provider wise growth rate of expected shares.