K-clique percolation in free association networks. The mechanism behind the $7 \pm 2 $ law ?

TL;DR

This paper investigates k-clique percolation in free association networks, revealing universal patterns and proposing a model that may explain Miller's 7±2 rule for working memory capacity.

Contribution

It introduces a new universality pattern in free association networks and a model extending preferential attachment to explain the observed percolation threshold.

Findings

k-clique percolation occurs for all k<k_c≈6-7 in SWOW-EN and Dutch networks

Proposes a new network evolution model extending preferential attachment

Suggests a qualitative explanation for Miller's 7±2 law

Abstract

It is important to reveal the mechanisms of propagation in different cognitive networks. In this study we discuss the k-clique percolation phenomenon on the free association networks including "English Small World of Words project" (SWOW-EN). We compare different semantic networks and networks of free associations for different languages. Surprisingly it turned out that $k$-clique percolation for all $k<k_c=(6-7)$ is possible on SWOW-EN and Dutch language network. Our analysis suggests the new universality patterns for a community organization of free association networks. We conjecture that our result can provide the qualitative explanation of the Miller's $7\pm 2$ rule for the capacity limit of working memory. The new model of network evolution extending the preferential attachment is suggested which provides the observed value of $k_c$.