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Decimation of Fast States and Weak Nodes: Topological Variation via Persistent Homology

  • Irene Donato
  • Giovanni Petri
  • Martina Scolamiero
  • Lamberto Rondoni
  • Francesco Vaccarino
Part of the Springer Proceedings in Complexity book series (SPCOM)

Abstract

We study the topological variation in Markov processes and networks due to a coarse-graining procedure able to preserve the Markovian property. Such coarse-graining method simplifies master equation by neglecting the fast states and significantly reduces the network size by decimating weak nodes.

We use persistent homology to identify the robust topological structure which survive after the coarse-graining.

Keywords

Markov processes Complex networks Coarse-graining (theory) Persistent homology Computational topology 

Notes

Acknowledgements

L. Rondoni gratefully acknowledges financial support from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant agreement No. 202680. The EC is not liable for any use that can be made on the information contained herein.

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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Irene Donato
    • 1
    • 2
  • Giovanni Petri
    • 1
  • Martina Scolamiero
    • 1
  • Lamberto Rondoni
    • 2
    • 3
  • Francesco Vaccarino
    • 1
    • 2
  1. 1.ISI FoundationTorinoItaly
  2. 2.Dipartimento di Scienze MatematichePolitecnico di TorinoTorinoItaly
  3. 3.INFNSezione di TorinoTorinoItaly

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