Persistent Homology of Complex Networks

Persistent Homology of Complex Networks. Horak, D., Maletić, S., & Rajković, M. 2009(03):P03034.

Long-lived topological features are distinguished from short-lived ones (considered as topological noise) in simplicial complexes constructed from complex networks. A new topological invariant, persistent homology, is determined and presented as a parameterized version of a Betti number. Complex networks with distinct degree distributions exhibit distinct persistent topological features. Persistent topological attributes, shown to be related to the robust quality of networks, also reflect the deficiency in certain connectivity properties of networks. Random networks, networks with exponential connectivity distribution and scale-free networks were considered for homological persistency analysis.

@article{horakPersistentHomologyComplex2009,
  langid = {english},
  title = {Persistent Homology of Complex Networks},
  volume = {2009},
  issn = {1742-5468},
  url = {http://stacks.iop.org/1742-5468/2009/i=03/a=P03034},
  doi = {10.1088/1742-5468/2009/03/P03034},
  abstract = {Long-lived topological features are distinguished from short-lived ones (considered as topological noise) in simplicial complexes constructed from complex networks. A new topological invariant, persistent homology, is determined and presented as a parameterized version of a Betti number. Complex networks with distinct degree distributions exhibit distinct persistent topological features. Persistent topological attributes, shown to be related to the robust quality of networks, also reflect the deficiency in certain connectivity properties of networks. Random networks, networks with exponential connectivity distribution and scale-free networks were considered for homological persistency analysis.},
  number = {03},
  journaltitle = {Journal of Statistical Mechanics: Theory and Experiment},
  shortjournal = {J. Stat. Mech.},
  urldate = {2018-04-16},
  date = {2009},
  pages = {P03034},
  author = {Horak, Danijela and Maletić, Slobodan and Rajković, Milan},
  file = {/home/dimitri/Nextcloud/Zotero/storage/IT5PKTTS/Horak et al. - 2009 - Persistent homology of complex networks.pdf}
}

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