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Communicability angles reveal critical edges for network consensus dynamics.

Ernesto Estrada1, Eusebio Vargas-Estrada1, Hiroyasu Ando2

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This summary is machine-generated.

Network topology significantly impacts consensus dynamics. Removing edges based on communicability angle or betweenness centrality slows consensus, with network density and average distance-sum explaining over 80% of consensus time variance.

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Area of Science:

  • Network Science
  • Complex Systems
  • Dynamical Processes

Background:

  • Consensus dynamics are crucial for collective behavior in networks.
  • Understanding how network topology influences these dynamics is essential.

Purpose of the Study:

  • To investigate the impact of network topological structure on consensus dynamical processes.
  • To identify critical network features affecting the time to reach consensus.

Main Methods:

  • Analysis of a large dataset of real-world networks.
  • Edge removal based on communicability angle and edge betweenness centrality.
  • Theoretical justification using algebraic connectivity and isoperimetric number.
  • Statistical analysis of global topological parameters (network density, average distance-sum).

Main Results:

  • Edge removal by communicability angle increased consensus time by 5.68x.
  • Edge removal by betweenness centrality increased consensus time by 3.70x.
  • Network density and average distance-sum explained >80% of consensus time variance.

Conclusions:

  • Network topology, particularly edge properties and global parameters, critically influences consensus dynamics.
  • Communicability angle and betweenness centrality are key indicators of critical edges for consensus.
  • Network density and average distance-sum are major determinants of consensus time.