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Network information and connected correlations.

Elad Schneidman1, Susanne Still, Michael J Berry

  • 1Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.

Physical Review Letters
|December 20, 2003
PubMed
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We introduce connected information, an information-theoretic measure for network correlations. This method quantifies irreducible N-point correlations by analyzing entropy changes, revealing how network elements collectively inform about external sources.

Area of Science:

  • Information Theory
  • Network Science
  • Statistical Mechanics

Background:

  • Entropy and information are fundamental measures of correlation within networks.
  • Existing methods for correlation analysis in networks have limitations in capturing complex interdependencies.

Purpose of the Study:

  • To develop an information-theoretic analog of connected correlation functions.
  • To quantify irreducible N-point correlations in a network.
  • To demonstrate the decomposition of information carried by network elements about an external source.

Main Methods:

  • Constructing irreducible N-point correlation measures based on entropy reduction.
  • Calculating "connected information" terms for joint probability distributions.
  • Comparing joint entropy with maximum entropy from N-1 variable distributions.

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Main Results:

  • Defined connected information as a decrease in joint entropy relative to maximum entropy.
  • Calculated connected information for several example networks.
  • Showcased the ability of connected information to decompose information flow from populations to external sources.

Conclusions:

  • Connected information provides a novel framework for analyzing complex correlations in networks.
  • This approach offers a principled way to understand information flow and redundancy within systems.
  • The method is applicable to diverse fields studying interconnected data.