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Area of Science:

  • Complex systems analysis
  • Network science
  • Graph theory

Background:

  • Laplacian eigenvectors of complex networks explain system dynamics.
  • Understanding eigenvector localization is key to complex system behavior.

Purpose of the Study:

  • To numerically examine the roles of higher-order and pairwise links in eigenvector localization of hypergraph Laplacians.
  • To elucidate how different link types influence localization patterns.

Main Methods:

  • Numerical examination of hypergraph Laplacians.
  • Analysis of eigenvector localization based on eigenvalue magnitude.
  • Comparison of higher-order versus pairwise link effects.

Main Results:

  • Pairwise interactions can cause eigenvector localization for small eigenvalues in certain cases.
  • Higher-order interactions consistently steer localization of eigenvectors for larger eigenvalues, irrespective of link density.
  • The influence of higher-order links persists even when they are less numerous than pairwise links.

Conclusions:

  • Eigenvector localization in complex networks is significantly influenced by the interplay of link types.
  • Distinguishing the roles of higher-order and pairwise links provides deeper insights into network dynamics.
  • These findings aid in understanding phenomena like diffusion and random walks on systems with complex interactions.