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Target Controllability of Two-Layer Multiplex Networks Based on Network Flow Theory.

Kun Song, Guoqi Li, Xumin Chen

IEEE Transactions on Cybernetics

|April 17, 2019

Summary

Controlling two-layer multiplex networks requires minimum control sources. This study introduces a maximum flow-based algorithm (MFTP) to efficiently identify the minimum sources needed for target controllability in complex networks.

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Area of Science:

Network Science
Control Theory
Complex Systems

Background:

Multiplex networks are prevalent in real-world systems.
Controlling these networks, especially layer-specific control, presents significant challenges.
Existing methods struggle with optimizing control source allocation in multi-layer networks.

Purpose of the Study:

To determine the minimum number of control sources for target controllability in two-layer multiplex networks.
To address the constraint that control sources interact with only one layer.
To develop an efficient algorithm for this optimization problem.

Main Methods:

Formulating the problem as a path cover problem.
Converting the path cover problem into a maximum network flow problem.
Developing and applying the maximum flow-based target path-cover (MFTP) algorithm.

Main Results:

The study proves that the target controllability issue is equivalent to a specific path cover problem.
The MFTP algorithm is rigorously shown to find the minimum number of control sources.
The MFTP algorithm efficiently solves the maximum network flow problem for this application.

Conclusions:

The MFTP algorithm provides an optimal solution for minimum control source allocation in two-layer multiplex networks.
This research offers a computationally efficient method for enhancing network controllability.
The findings have broad implications for the target control of various real-world network systems.