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Input graph: the hidden geometry in controlling complex networks.

Xizhe Zhang1, Tianyang Lv2,3, Yuanyuan Pu1

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We introduce the input graph, a novel geometric tool to understand control schemes in complex networks. This method reveals relationships between input nodes and aids in designing effective network control strategies.

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Area of Science:

  • Network science
  • Control theory
  • Graph theory

Background:

  • Controlling complex networks (social, technological) requires understanding their intricate nature.
  • Numerous control schemes exist, prompting investigation into the relationships between input nodes.

Purpose of the Study:

  • To introduce the input graph as a geometric framework to reveal complex relationships between control schemes and input nodes.
  • To provide a topological explanation for phenomena like bifurcation in dense networks.
  • To enable the design of efficient methods for altering node control types.

Main Methods:

  • Development of the 'input graph' concept.
  • Mathematical proofs demonstrating properties of the input graph.
  • Analysis of input graphs in real-world networks.

Main Results:

  • The input graph clarifies the complex relationships among all possible input nodes and control schemes.
  • Adjacent nodes in the input graph share control types (either all controllable or not).
  • Emergence of giant components in input graphs of real networks explains bifurcation phenomena.

Conclusions:

  • The input graph offers fundamental insights into complex network control principles.
  • This framework provides a general mechanism for designing tailored control schemes for diverse applications.