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Beyond non-backtracking: non-cycling network centrality measures.

Francesca Arrigo1, Desmond J Higham2, Vanni Noferini3

  • 1Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, UK.

Proceedings. Mathematical, Physical, and Engineering Sciences
|April 10, 2020
PubMed
Summary
This summary is machine-generated.

This study introduces non-backtracking walks and a novel recursive method to analyze network centrality. These methods offer practical applications for large-scale network analysis by systematically removing cycles.

Keywords:
Hashimoto matrixcentrality indexcomplex networkdeformed graph Laplaciangenerating functionmatrix polynomial

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Area of Science:

  • Graph theory
  • Network science
  • Theoretical computer science
  • Stochastic analysis
  • Physics

Background:

  • Non-backtracking walks, which avoid immediate revisits, offer benefits for network centrality measures.
  • Traditional walk-based centrality measures can be enhanced by imposing non-backtracking constraints.

Purpose of the Study:

  • To characterize and generalize non-backtracking centrality measures using the Hashimoto matrix construction.
  • To develop a recursive method for systematically removing cycles (triangles, squares, etc.) from network walks.
  • To explore the extension of universality results for classical walk-based centrality to non-cycling cases.

Main Methods:

  • Utilizing the Hashimoto matrix construction to define and study non-backtracking centrality.
  • Developing a recursive extension to systematically eliminate cycles of increasing length.
  • Analyzing the spectral radius of matrix power series to understand limiting behavior.

Main Results:

  • The Hashimoto matrix construction provides a framework for characterizing generalized non-backtracking centrality.
  • The recursive extension effectively removes cycles, leading to new centrality measures.
  • Universality results for classical walk-based centrality extend to these non-cycling measures.

Conclusions:

  • The proposed recursive construction yields practical centrality measures applicable to large-scale networks.
  • This work advances the understanding of non-backtracking walks and their role in network analysis.