Biol., ecol., social, and technol. systems are complex structures with multiple interacting parts, often represented by networks. Correlation matrixes describing interdependency of the variables in such structures provide key information for comparison and classification of such systems. Classification based on correlation matrixes could supplement or improve classification based on variable values, since the former reveals similarities in system structures, while the latter relies on the similarities in system states. Importantly, this approach of clustering correlation matrixes is different from clustering elements of the correlation matrixes, because our goal is to compare and cluster multiple networks - not the nodes within the networks. A novel approach for clustering correlation matrixes, named "snakes-&-dragons," is introduced and illustrated by examples from neuroscience, human microbiome, and macroeconomics.