Value of peripheral nodes in controlling multilayer scale-free networks

Area of Science:

• Network Science
• Complex Systems
• Control Theory

Background:

• Two-layer networks are prevalent in real-world systems.
• Controlling such networks is crucial for understanding their dynamics.
• Node importance is often defined by degree, distinguishing central from peripheral nodes.

Purpose of the Study:

• To analyze the controllability of a two-layer scale-free network.
• To investigate the impact of node selection (peripheral vs. central) on controllability.
• To evaluate the cost-efficiency of different control strategies.

Main Methods:

• Numerical simulations were employed to study network controllability.
• A weighted importance value (w) was assigned to nodes based on in-degree and out-degree.
• Peripheral nodes (low w) and central nodes (high w) were analyzed as driver nodes and for inter-layer connections.

Main Results:

• Selecting low importance (w) nodes to connect layers increases the controllable network portion.
• Peripheral nodes are as effective as central nodes when acting as driver nodes.
• Utilizing peripheral nodes for inter-layer connections or as drivers is the most cost-efficient and performs best.

Conclusions:

• Peripheral nodes offer a highly effective and economical strategy for controlling two-layer networks.
• Node importance, defined by degree, significantly influences network control and cost-efficiency.
• The findings suggest optimizing control strategies by focusing on less central network components.