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Beyond Topological Persistence: Starting from Networks

Author

Listed:
  • Mattia G. Bergomi

    (Veos Digital, 20124 Milan, Italy)

  • Massimo Ferri

    (Advanced Research Center on Electronic Systems “E. De Castro”, Department of Mathematics, Università di Bologna, 40126 Bologna, Italy)

  • Pietro Vertechi

    (Veos Digital, 20124 Milan, Italy)

  • Lorenzo Zuffi

    (Advanced Research Center on Electronic Systems “E. De Castro”, Department of Mathematics, Università di Bologna, 40126 Bologna, Italy)

Abstract

Persistent homology enables fast and computable comparison of topological objects. We give some instances of a recent extension of the theory of persistence, guaranteeing robustness and computability for relevant data types, like simple graphs and digraphs. We focus on categorical persistence functions that allow us to study in full generality strong kinds of connectedness—clique communities, k -vertex, and k -edge connectedness—directly on simple graphs and strong connectedness in digraphs.

Suggested Citation

  • Mattia G. Bergomi & Massimo Ferri & Pietro Vertechi & Lorenzo Zuffi, 2021. "Beyond Topological Persistence: Starting from Networks," Mathematics, MDPI, vol. 9(23), pages 1-15, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3079-:d:691263
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    References listed on IDEAS

    as
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    2. Toivonen, Riitta & Onnela, Jukka-Pekka & Saramäki, Jari & Hyvönen, Jörkki & Kaski, Kimmo, 2006. "A model for social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(2), pages 851-860.
    3. Gergely Palla & Albert-László Barabási & Tamás Vicsek, 2007. "Quantifying social group evolution," Nature, Nature, vol. 446(7136), pages 664-667, April.
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