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Continuous-time quantum walk based centrality testing on weighted graphs.

Yang Wang1, Shichuan Xue1, Junjie Wu2

  • 1Institute for Quantum Information & State Key Laboratory of High Performance Computing, College of Computer Science and Technology, National University of Defense Technology, Changsha, 410073, China.

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Summary
This summary is machine-generated.

This study extends continuous-time quantum walk centrality to weighted graphs, showing high consistency with classical measures. This quantum centrality offers better distinguishing ability for important network vertices.

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Area of Science:

  • Network analysis
  • Quantum computation
  • Graph theory

Background:

  • Centrality measures are crucial in network analysis across various scientific domains.
  • Existing quantum centrality measures often overlook edge weights, which are vital in real-world networks.
  • There is a need for quantum centrality methods applicable to weighted graphs.

Purpose of the Study:

  • To extend the continuous-time quantum walk centrality measure to weighted graphs.
  • To evaluate the feasibility and reliability of this extended quantum centrality.
  • To compare its performance against classical centrality measures.

Main Methods:

  • Developed a continuous-time quantum walk centrality measure for weighted graphs.
  • Tested the measure on an ensemble of 41,675 graphs with diverse topologies.
  • Compared the quantum centrality rankings with eigenvector centrality using Vigna's correlation index.

Main Results:

  • Achieved an average Vigna's correlation index of 0.967, demonstrating strong consistency with eigenvector centrality.
  • Confirmed intuitive agreement in top-ranked vertices between quantum and classical centrality measures on large-scale weighted graphs.
  • Observed a wider range of centrality values for the quantum measure, indicating superior distinguishing ability.

Conclusions:

  • The continuous-time quantum walk centrality measure is effective and reliable for weighted graphs.
  • This quantum approach offers enhanced ability to identify important vertices compared to classical methods.
  • The findings support the broader applicability of quantum computation in network analysis.