Social percolation revisited: From 2d lattices to adaptive networks

The social percolation model Solomon et al. (2000) considers a 2-dimensional regular lattice. Each site is occupied by an agent with a preference x_i sampled from a uniform distribution U [ 0 , 1 ] . Agents transfer the information about the quality q of a movie to their neighbors only if x_i ≤ q . Information percolates through the lattice if q =q_c = 0 . 593 . - From a network perspective the percolating cluster can be seen as a random-regular network with n_c nodes and a mean degree that depends on q_c. Preserving these quantities of the random-regular network, a true random network can be generated from the G(n , p) model after determining the link probability p. I then demonstrate how this random network can be transformed into a threshold network, where agents create links dependent on their x_i values. Assuming a dynamics of the x_i and a mechanism of group formation, I further extend the model toward an adaptive social network model.