Node-layer duality in multilayer networks

Multilayer networks (MNs) constitute an efficient model paradigm for complex systems described over several interacting dimensions, levels or scales.

It has been shown that MNs are invariant by describing layers as nodes and vice versa. We call node-layer duality the concept that the interacting entities are either nodes or layers depending on the description we adopt. Node-layer duality allows to study consistently the same system with two dual descriptions, one of which being systematically overlooked in MNs topological study.

To evaluate the potential of this framework, we propose two normalized Euclidean distances between MNs, based on the multidegree of the related interacting entities for each description. To systematically investigate distances, we derive analytically a multilevel stochastic rewiring algorithm. Main results show that a given description distinguishes better topologically different MNs depending on their organizational differences. Also, only the dual analysis is able to capture every such differences.

Our approach can provide a multilevel comparative analysis between normal and abnormal states (brain networks) as well as a better characterization of MN in any topological studies.