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Maximum entropy in dynamic complex networks.

Noam Abadi1, Franco Ruzzenenti1

  • 1Integrated Research on Energy, Environment and Society, Faculty of Science and Engineering, <a href="https://ror.org/012p63287">University of Groningen</a>, Groningen, Netherlands.

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Summary
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This study introduces a novel information-theoretic approach for dynamic complex networks, extending beyond stationary models. The maximum caliber method accurately describes network evolution, aligning with stochastic simulations and established principles.

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Area of Science:

  • Complex Networks
  • Network Science
  • Information Theory

Background:

  • Complex networks analyze interacting systems, often using randomization for property understanding.
  • Existing information-theoretic randomization methods are limited to stationary network descriptions.
  • Stochastic randomization methods for dynamic networks lack general theoretical foundations.

Purpose of the Study:

  • To extend information-theoretic methods for analyzing dynamic complex network models.
  • To construct dynamic network ensemble distributions using the maximum caliber principle.
  • To validate these distributions against stochastic randomization simulations.

Main Methods:

  • Applied the information-theoretic principle of maximum caliber to construct dynamic network ensembles.
  • Used constraints representing known statistical properties (e.g., average degree) throughout network evolution.
  • Compared maximum caliber distributions with simulations of stochastic randomization under identical constraints.

Main Results:

  • Ensemble distributions derived from simulations closely matched those calculated using the maximum caliber principle.
  • Converged equilibrium distributions agreed with established maximum entropy results for the given constraints.
  • Demonstrated the efficacy of maximum caliber for dynamic network analysis beyond stationary models.

Conclusions:

  • The maximum caliber principle provides a robust framework for information-theoretic analysis of dynamic complex networks.
  • This approach bridges the gap between stationary information-theoretic methods and dynamic stochastic processes.
  • Future research can explore further connections to maximum entropy and other network dynamics approaches.