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Topological structures are consistently overestimated in functional complex networks.

Massimiliano Zanin1,2, Seddik Belkoura3, Javier Gomez4

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Bayesian inference offers a new way to analyze complex networks, like the human brain, by accounting for data uncertainty. Ignoring this uncertainty leads to inaccurate network structures, especially with limited data.

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Area of Science:

  • Neuroscience
  • Network Science
  • Computational Biology

Background:

  • Complex networks, particularly brain networks, are crucial for understanding system dynamics.
  • Traditional frequentist methods for network reconstruction ignore data uncertainty, leading to potential biases.
  • The finiteness of data introduces uncertainty in estimating network structures.

Purpose of the Study:

  • To introduce a Bayesian inference approach for reconstructing functional complex networks.
  • To quantify the impact of link uncertainty on network topology.
  • To develop a method for correcting topological biases in frequentist network analysis.

Main Methods:

  • Link weights treated as random variables with probability distributions.
  • Ensemble of networks sampled from Bayesian posterior distributions.
  • Statistical and topological analyses to assess the role of uncertainty.
  • Validation using synthetic and real-world brain activity data.

Main Results:

  • Link uncertainty is equivalent to random rewiring, and its omission causes overestimation of topological structures.
  • Bias is amplified in shorter time series, indicating a potential time resolution limit for reliable network reconstruction.
  • A sampling process is proposed to correct frequentist network topological values.

Conclusions:

  • Bayesian inference provides a more accurate method for reconstructing complex networks by incorporating data uncertainty.
  • Frequentist approaches can lead to significant topological overestimation, particularly with limited data.
  • The study highlights the importance of accounting for uncertainty in network science, with implications for neuroscience and other fields.