Network motifs: A key variable in the equation of dynamic flow between macro and micro layers in Complex Networks

Abstract Complex Networks theory represents a powerful tool to model real-world systems as graphs with non-trivial topological features. Static by their definition, complex networks are limited to be the reflection or the snapshot of the dynamical systems they encode in a given moment. Frankly, studies show that the network preserves the characteristics of the dynamic flow between various structures evolved at different scales: micro, meso, and macro, respectively. Considering that micro components will end by encapsulating any stability state initiated by a perturbation of the macroscale, the most popular framework used to analyze complex networks associates in a reverse-engineering manner properties of the micro-scale components with global network characteristics. Although the principle of convergence is widely agreed upon, we consider the transition from micro to macro one not studied enough, and the highlighting of an in-between layer being necessary exemplifies the convergence mechanism better. Our work is willing to improve existing approaches of understanding the intricate beauty behind network dynamics by embracing the chaos they evolve and not order it using inflexible analytical mechanisms. We formulate a series of research questions that are willing to demonstrate that the existence of a mesoscale structure, namely network motifs, is connected with a variety of microscale, respectively, macroscale properties - hence strengthening the proof of macro-meso-micro convergence. Our approach could provide a substantial improvement in the models used to understand molecular self-assembly, protein-based cellular adaptation, social interactions, and many other fields, where connections between structures or components play an essential role.

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