Social percolation revisited: From 2d lattices to adaptive networks

TL;DR

This paper revisits the social percolation model, extending it from 2D lattices to adaptive networks by incorporating network transformations and agent dynamics, revealing new insights into information spread and group formation.

Contribution

It introduces a novel framework that transforms traditional lattice-based social percolation into adaptive networks with dynamic agent interactions.

Findings

Percolation threshold at q=0.593 on 2D lattices.

Network transformations preserve key percolation properties.

Adaptive network model captures dynamic group formation.

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 $x_{i}\leq q$. 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.