The evolution and de Bruijn matrices are sparse, both in their normal and in their probabilistic versions; that is a consequence of their origins as connectivity matrices of diagrams of one type or another. It is therefore natural to seek a description of such matrices in terms of the visual properties of the same diagrams, one of the most evident of which is the network of cycles or loops which they contain. It is even more satisfying if the description will accommodate the accumulation of a variety of matrices into families. A recent article of Cvitanovic [31] reveals the process, as applied to an analysis of strange attractors.

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