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It is important to reveal the mechanisms of propagation in different cognitive networks. In this study, we discuss the k-clique percolation phenomenon as related to the free association networks including the English Small World of Words project (SWOW-EN). We compared different semantic networks and networks of free associations for various languages. Surprisingly, k-clique percolation for all    $$k&lt;k_c=$$  k &lt; k c = 6–7 is possible on free association networks of different languages. Our analysis suggests new universality patterns for a community organization of free association networks. We conjecture that our result can provide a qualitative explanation of Miller’s    $$7\pm 2$$  7 ± 2 rule for the capacity limit of working memory. A new model of network evolution extending the preferential attachment is suggested, providing the observed value of    $$k_c$$  k c .

K-clique percolation in free association networks and the possible mechanism behind the $$7 \pm 2$$ law