The relationship between structure and control in multiplex networks

Multiplex networks are abstract representations of those complex systems in which multiple types of relationships exist amongst components. The control properties of such networks in response to perturbations can be understood in the framework of network control theory. In control tasks where the control signals are injected into a specific `input' layer, how are the control properties of a target layer determined by its structure and its relationship with the input layer? Here, we characterize the structure of multiplex networks in terms of the eigenspectra of individual layers and the alignment between their eigenmodes, and determine the dependence of control energy on these structural parameters. We study the role of layer density, layer topology, and interlayer alignment in determining the control properties of duplex networks with the layers constructed from the networks of different topologies. Further, we investigate the role of the alignment between the eigenmodes of the `input' layer and the `target' layer in setting the control cost of specific modes of the target layer. We discuss the applications of our results in understanding the layered architecture of brain networks from the perspective of control.