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 xi sampled from a uniform distribution U[0,1]. Agents transfer the information about the quality q of a movie to their neighbors only if xi≤q. Information percolates through the lattice if q=qc=0.593. – From a network perspective the percolating cluster can be seen as a random–regular network with nc nodes and a mean degree that depends on qc. 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 xi values. Assuming a dynamics of the xi and a mechanism of group formation, I further extend the model toward an adaptive social network model.