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Network communities can emerge without node heterogeneity. This study introduces the Ramsey community number (rκ) to define the minimum graph size for guaranteed community emergence, showing local network rules drive this property.

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Area of Science:

  • Network Science
  • Graph Theory
  • Computational Social Science

Background:

  • Natural systems are often modeled as networks with segregated communities.
  • Node heterogeneity (e.g., political affiliation, biological function) is traditionally considered essential for community segregation.

Purpose of the Study:

  • To investigate if node heterogeneity is a necessary requirement for network community formation.
  • To introduce a quantitative measure for guaranteed community emergence.

Main Methods:

  • Numerical simulations using the stochastic block model and Infomap for community detection.
  • Introduction of the Ramsey community number (rκ) as the minimum graph size for near-certain community emergence.

Main Results:

  • Node heterogeneity is not a necessary condition for the emergence of network communities.
  • Networks generated by local rules exhibit finite rκ values, indicating emergent communities.
  • Randomized networks lack emergent communities, unlike those formed by local rules.

Conclusions:

  • Network communities are an emergent property driven by local network evolution rules, not solely by node heterogeneity.
  • The Ramsey community number (rκ) provides a theoretical framework for understanding community emergence thresholds.