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High modularity in complex networks decreases robustness. Conversely, low modularity in modular d-regular graphs enhances network robustness and path efficiency, offering a balance between connectivity and structure.

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Area of Science:

  • Network science
  • Graph theory
  • Complex systems analysis

Background:

  • Research on network robustness and modularity often focuses on Erdos-Renyi and Scale-Free networks.
  • Existing studies primarily examine networks with Poisson or power-law degree distributions.

Purpose of the Study:

  • To investigate the impact of modularity on the robustness of modular d-regular graphs.
  • To analyze the trade-offs between modularity, robustness, and path efficiency in these specific network structures.

Main Methods:

  • Analysis of modular d-regular graphs.
  • Comparison of robustness across different modularity levels.
  • Evaluation of average path length to assess small-world properties.

Main Results:

  • High modularity significantly reduces network robustness compared to random d-regular graphs.
  • Low modularity in d-regular graphs leads to the small-world property with an average path length of O(logN).
  • The study isolates the effect of modularity on robustness, independent of degree distribution variations.

Conclusions:

  • High modularity is detrimental to network robustness in modular d-regular graphs.
  • Low modularity promotes a beneficial coexistence of high robustness and efficient path lengths.
  • Findings suggest that optimizing modularity is crucial for designing robust and efficient complex networks.