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Constructing directed networks with a desired minimum balanced coloring.

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We developed a new algorithm for generating directed networks with specific symmetries. This method expands nodes into clusters, ensuring structural identity for creating synthetic networks with controlled symmetries.

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Area of Science:

  • Network Science
  • Graph Theory
  • Computational Biology

Background:

  • Empirical networks in biological, social, and technological systems exhibit node symmetries.
  • Existing network generation algorithms often fail to control for emergent symmetries.

Purpose of the Study:

  • To present an algorithm for generating "expanded" directed networks with user-defined symmetries.
  • To provide analytical conditions for feasible network expansion.

Main Methods:

  • Algorithm development for directed network expansion.
  • Transformation of base network nodes into clusters.
  • Feasibility checks for expansion and minimal expansion.

Main Results:

  • The algorithm successfully generates directed networks with prescribed symmetries.
  • Analytical conditions for feasibility and minimal expansion were established.
  • Synthetic networks with controlled symmetries were constructed.

Conclusions:

  • The presented algorithm offers a method to generate directed networks with specific symmetries.
  • This approach facilitates the creation of synthetic networks for studying symmetry-related phenomena.