Social percolation revisited: from 2d lattices to adaptive networks. (English) Zbl 07458589
Summary: 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 \(x_i \leq q\). 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.
MSC:
| 82-XX | Statistical mechanics, structure of matter |
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