Exact Coupling Threshold for Structural Transition in Interconnected Networks

TL;DR

This paper derives an exact analytical expression for the coupling threshold in interconnected networks, clarifying the transition point between distinguishable and indistinguishable network regimes, which is vital for understanding their structural behavior.

Contribution

It provides the first precise analytical formula for the coupling threshold in interconnected networks, advancing the theoretical understanding of their structural transition.

Findings

Derived an exact formula for the coupling threshold

Identified the implications of the threshold on network interrelation

Enhanced understanding of structural transitions in interconnected systems

Abstract

Interconnected networks are mathematical representation of systems where two or more simple networks are coupled to each other. Depending on the coupling weight between the two components, the interconnected network can function in two regimes: one where the two networks are structurally distinguishable, and one where they are not. The coupling threshold--denoting this structural transition--is one of the most crucial concepts in interconnected networks. Yet, current information about the coupling threshold is limited. This letter presents an analytical expression for the exact value of the coupling threshold and outlines network interrelation implications.