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