Permutation Entropy for Graph Signals

John Stewart Fabila Carrasco*, Chao Tan, Javier Escudero

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Entropy metrics (for example, permutation entropy) are nonlinear measures of irregularity in time series (one-dimensional data). Some of these entropy metrics can be generalised to data on periodic structures such as a grid or lattice pattern (two-dimensional data) using its symmetry, thus enabling their application to images. However, these metrics have not been developed for signals sampled on irregular domains, defined by a graph. Here, we define for the first time an entropy metric to analyse signals measured over irregular graphs by generalising permutation entropy, a well-established nonlinear metric based on the comparison of neighbouring values within patterns in a time series. Our algorithm is based on comparing signal values on neighbouring nodes, using the adjacency matrix. We show that this generalisation preserves the properties of classical permutation for time series and the recent permutation entropy for images, and it can be applied to any graph structure with synthetic and real signals. We expect the present work to enable the extension of other nonlinear dynamic approaches to graph signals.
Original languageEnglish
Pages (from-to)288-300
Number of pages13
JournalIEEE Transactions on Signal and Information Processing Over Networks
Early online date13 Apr 2022
Publication statusE-pub ahead of print - 13 Apr 2022


  • Graph signal processing
  • graph Laplacian
  • permutation entropy
  • adjacency matrix
  • Nonlinearity dynamics
  • Topology
  • Entropy metric
  • Irregularity
  • Adjacency matrix
  • Nonlinearity Dynamics
  • Graph Laplacian
  • Permutation entropy


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