Motifs stability in hierarchical modular networks

Recent advances in our understanding of information processing in biological systems have highlighted the importance of modularity in the underlying networks (ranging from metabolic to neural networks), as well as the crucial existence of motifs, namely small circuits (not necessary loopy) whose empirical presence in these networks is statistically high. In these notes, mixing statistical mechanical with graph theoretical perspectives and restricting on hierarchical modular networks, we analyze the stability of key motifs that naturally emerge and we prove that all the loopy structures have systematically a broader steadiness with respect to loop-free motifs.