Social percolation revisited: From 2d lattices to adaptive networks

Abstract

The social percolation model \citep{solomon-et-00} 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 $x_i\le q$. 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.

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