Persistent homology of complex networks

By Danijela Horak, S. Maletić, M. Rajković. 2008

223 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5aa6812c48455a463e57ad41526dcc997209286c

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In Computational Theory and Mathematics

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Higher order interactions in complex networks of phase oscillators promote abrupt synchronization switching (2019, background): “Recently, the network science community has turned its attention to simplicial geometry to better represent the kinds of interactions that one can find beyond typical pairwise interactions [20].”
Persistent homology analysis of protein structure, flexibility and folding (2014, background): “It has been applied to a variety of domains, including image analysis [48–51], image retrieval [52], chaotic dynamics verification [53, 54], sensor network [55], complex network [56, 57], data analysis [58–62], computer vision [50], shape recognition [63], and computational biology [64–66].”
Cliques and cavities in the human connectome (2016, background): “Though comparing persistent homology of weighted networks at the global level has been successful (for example Benzekry et al. 2015; Horak et al. 2009), scrutinizing individual persistent features may have more clinical relevance due to their size and understandability.”
Homological scaffolds of brain functional networks (2014, background): “Similar approaches to brain data [42,43], collaboration data [44] and network structure [45] also exist.”
A roadmap for the computation of persistent homology (2015, methodology): “See the book [69] for an overview of such methods, and see the paper [68] for an overview of PH for networks.”