<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>The method of isospectral network reduction allows one the ability to reduce a network while preserving the network’s spectral structure. In this paper we describe a number of recent applications of the theory of isospectral reductions. This includes finding hidden structures, specifically latent symmetries, in networks, uncovering different network hierarchies, and simultaneously determining different network cores. We also specify how such reductions can be interpreted as dynamical systems and describe the type of dynamics such systems have. Additionally, we show how the recent theory of equitable decompositions can be paired with the method of isospectral reductions to decompose networks.</p></abstract>

The method of isospectral network reduction allows one the ability to reduce a network while preserving the network’s spectral structure. In this paper we describe a number of recent applications of the theory of isospectral reductions. This includes finding hidden structures, specifically latent symmetries, in networks, uncovering different network hierarchies, and simultaneously determining different network cores. We also specify how such reductions can be interpreted as dynamical systems and describe the type of dynamics such systems have. Additionally, we show how the recent theory of equitable decompositions can be paired with the method of isospectral reductions to decompose networks.

Finding Hidden Structures, Hierarchies, and Cores in Networks via Isospectral Reduction

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

The method of isospectral network reduction allows one the ability to reduce a network while preserving the network’s spectral structure. In this paper we...

Finding Hidden Structures, Hierarchies, and Cores in Networks via Isospectral Reduction

Article Category: Papers dedicated to the memory of Valetnin Afraymovich (1945-2018)

Published Online: Jun 28, 2019

Page range: 231 - 254

Received: Aug 19, 2018

Accepted: Nov 19, 2018

DOI: https://doi.org/10.2478/AMNS.2019.1.00021

Keywords
Isospectral Network Reductions, Latent Symmetry, Network Hierarchy, Network Core, Equitable Decomposition

© 2019 Leonid Bunimovich et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Finding Hidden Structures, Hierarchies, and Cores in Networks via Isospectral Reduction

Article Category: Papers dedicated to the memory of Valetnin Afraymovich (1945-2018)

Published Online: Jun 28, 2019

Page range: 231 - 254

Received: Aug 19, 2018

Accepted: Nov 19, 2018

DOI: https://doi.org/10.2478/AMNS.2019.1.00021

KeywordsIsospectral Network Reductions, Latent Symmetry, Network Hierarchy, Network Core, Equitable Decomposition

© 2019 Leonid Bunimovich et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Isospectral Network Reductions, Latent Symmetry, Network Hierarchy, Network Core, Equitable Decomposition