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The topology of the directed clique complex as a network invariant

Type of publication Peer-reviewed
Publikationsform Original article (peer-reviewed)
Publication date 2016
Author Masulli Paolo, Villa Alessandro E.P.,
Project NeurEcA: Does working memory training affect decision making? A NeuroEconomic study of ADHD adults and healthy controls
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Original article (peer-reviewed)

Journal SpringerPlus
Volume (Issue) 5
Page(s) 388
Title of proceedings SpringerPlus
DOI 10.1186/s40064-016-2022-y

Open Access

Abstract

We introduce new algebro-topological invariants of directed networks, based on the topological construction of the directed clique complex. The shape of the underlying directed graph is encoded in a way that can be studied mathematically to obtain network invariants such as the Euler characteristic and the Betti numbers. Two different cases illustrate the application of the Euler characteristic. We investigate how the evolution of a Boolean recurrent artificial neural network is influenced by its topology in a dynamics involving pruning and strengthening of the connections, and to show that the topological features of the directed clique complex influence the dynamical evolution of the network. The second application considers the directed clique com- plex in a broader framework, to define an invariant of directed networks, the network degree invariant, which is constructed by computing the topological invariant on a sequence of sub-networks filtered by the minimum in- or out-degree of the nodes. The application of the Euler characteristic presented here can be extended to any directed network and provides a new method for the assessment of specific functional features associated with the network topology.
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