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Detectability threshold in weighted modular networks.

Filippo Radicchi1, Filipi N Silva1, Alessandro Flammini1

  • 1Indiana University, Center for Complex Networks and Systems Research, Luddy School of Informatics, Computing, and Engineering, Bloomington, Indiana 47408, USA.

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Summary
This summary is machine-generated.

Detecting community structure in networks is possible up to a certain mixing threshold. This threshold depends on node degree and edge weight distributions, with higher variability in weights hindering detection.

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Area of Science:

  • Network science
  • Statistical physics
  • Data analysis

Background:

  • Community detection algorithms aim to identify groups of nodes in networks.
  • The weighted planted-partition model is a standard benchmark for evaluating community detection methods.
  • Spectral modularity optimization is a common technique for community detection.

Purpose of the Study:

  • To determine the necessary conditions for detecting ground-truth partitions in weighted networks.
  • To analytically derive the maximum mixing level tolerated by spectral modularity optimization.
  • To investigate the impact of different edge-weight distributions on community detectability.

Main Methods:

  • Analytical derivation of the detectability threshold.
  • Analysis of the weighted planted-partition model with two equally sized communities.
  • Comparison of five edge-weight distributions (Dirac, Poisson, exponential, geometric, signed Bernoulli) under Poisson-distributed node degrees.

Main Results:

  • The detectability threshold depends on the first two moments of node degree and edge weight distributions.
  • Dirac distributed weights result in the smallest detectability threshold.
  • Exponentially distributed weights increase the threshold by a factor of sqrt[2]; higher weight variability can decrease detectability.

Conclusions:

  • Edge weight variability significantly influences the detectability of community structure.
  • Incorporating edge weights is detrimental when they do not carry information about the community structure.
  • The findings provide insights into the limitations and performance of spectral modularity optimization in weighted networks.