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Asymmetric community sizes in networks eliminate the detectability transition for small networks. For larger networks, asymmetry improves community detection accuracy by enabling local neighborhood analysis.

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Area of Science:

  • Network science
  • Statistical physics
  • Computer science

Background:

  • A phase transition in network community detection limits algorithmic success.
  • Previous findings were restricted to networks with uniform community sizes or degrees.

Purpose of the Study:

  • To investigate community detection in networks with asymmetric group sizes or average degrees.
  • To determine the impact of asymmetry on the detectability transition.

Main Methods:

  • Application of the cavity method.
  • Analysis of local neighborhood information.

Main Results:

  • Asymmetry completely removes the detectability transition for networks with up to four groups.
  • For more than four groups, the transition persists up to a critical asymmetry level.
  • This critical point aligns with the percolation of local information, enabling a global accuracy improvement.

Conclusions:

  • Network asymmetry significantly impacts community detection.
  • Local information analysis is key to overcoming detectability limits in asymmetric networks.