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Area of Science:

  • Network Science
  • Markov Chains
  • Data Mining

Background:

  • Node ranking is crucial in random networks.
  • Markov chains model network dynamics but have unknown transition matrices.
  • Learning network properties requires efficient sampling strategies.

Purpose of the Study:

  • To develop a dynamic sampling procedure for node ranking in random networks.
  • To decompose the network's Markov chain into ergodic classes.
  • To select the best node within each identified ergodic class.

Main Methods:

  • Defining a Markov chain for the random network.
  • Learning the transition probability matrix through random node interactions.
  • Implementing a dynamic sampling procedure with probability guarantees.
  • Maximizing a weighted probability for selecting the best node in each class.

Main Results:

  • The proposed dynamic sampling procedure ensures a probability guarantee for correct Markov chain decomposition.
  • The method effectively maximizes the weighted probability of selecting the best node from each ergodic class.
  • Numerical experiments validate the efficiency of the developed sampling strategy.

Conclusions:

  • The dynamic sampling procedure is an efficient method for node ranking in random networks.
  • This approach provides a robust framework for analyzing and optimizing network structures.
  • The findings contribute to advancements in network analysis and machine learning algorithms.