Metaplex networks: Influence of the exo-endo structure of complex systems on diffusion

Ernesto Estrada, Gissell Estrada-Rodriguez, Heiko Gimperlein

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)
89 Downloads (Pure)


In a complex system, the interplay between the internal structure of its entities and their interconnection may play a fundamental role in the global functioning of the system. Here, we define the concept of metaplex, which describes such a trade-off between the internal structure of entities and their interconnections. We then define a dynamical system on a metaplex and study diffusive processes on it. We provide analytical and computational evidence on the role played by the size of the nodes, the location of the internal coupling areas, and the strength and range of the coupling between the nodes on the global dynamics of metaplexes. Finally, we extend our analysis to two real-world metaplexes: a landscape and a brain metaplex. We corroborate that the internal structure of the nodes in a metaplex can dominate the global dynamics (brain metaplex) or play a regulatory role (landscape metaplex) in the influence of the interconnection between nodes.

Original languageEnglish
Pages (from-to)617-645
Number of pages29
JournalSIAM Review
Issue number3
Early online date6 Aug 2020
Publication statusPublished - 2020


  • Complex networks
  • D-path Laplacian
  • Diffusion
  • Metaplex network

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Mathematics
  • Applied Mathematics


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