# Persistent homology of complex networks

@article{Horak2009PersistentHO, title={Persistent homology of complex networks}, author={Danijela Horak and Slobodan Maleti{\'c} and Milan Rajkovi{\'c}}, journal={Journal of Statistical Mechanics: Theory and Experiment}, year={2009}, volume={2009}, pages={03034} }

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…

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