Innovation diffusion, influence propagation or ‘viral marketing’ is one of the most researched subject of contemporary era.
Compartmental models studying the spread of epidemics, which have susceptible (S), infected (I) and recovered (R) ‘SIR states’ are used to study the influence propagation in the electronic social networks as well. Initially these are descriptive models to describe a specific behavior of nodes when exposed to new innovation or information each node has an initial probability to adapt to that innovation. As each node adapts to the new innovation it has a specific amount of influence on the nodes connected to it.
Primarily two basic models are used to study the spread in a social network. An initial set of ‘active’ nodes at time t0 exert influence on the connected nodes and at t1 some of the connected nodes will become ‘active’ with a probability p(i). Each individual node has a threshold θi and when the influence from the neighbors is more than this threshold it becomes active. This model is called ‘Linear Threshold’ model. At each step, the set of nodes till the step – 1 remain active and influence their neighbors with a weightage. In independent cascade model each node is given only one chance to influence its neighbor.
Based on the above two diffusion models, the maximization problem is to determine the best set of initial ‘active’ nodes in a network to arrive at a best propagation by maximizing influence for ‘viral marketing’ campaign.
It is a NP-hard problem and this paper - http://pdf.aminer.org/000/472/900/maximizing_the_spread_of_influence_through_a_social_network.pdf discusses some interesting approximation algorithm with a general cascade, threshold and triggering models.
Have a good weekend reading!