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 ± 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 .