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Symmetry 2018, 10(7), 260; https://doi.org/10.3390/sym10070260

Schützenberger Symmetries in Network Structures

Electromagnetic and Sensor Systems Department, Naval Surface Warfare Center Dahlgren Division, 18444 Frontage Road Suite 327, Dahlgren, VA 22448-5161, USA
Received: 6 June 2018 / Revised: 25 June 2018 / Accepted: 29 June 2018 / Published: 4 July 2018
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Abstract

It is known that the set of all networks of fixed order form a semigroup. This fact provides for the Green’s L, R, H and equivalence equivalence classifications of all such networks. These classifications reveal certain structural invariants common to all networks within a Green’s equivalence class and enables the computation of the associated invariant preserving symmetries that transform a network into another network within a Green’s equivalence class. Here, the notion of Schützenberger symmetries in network structures is introduced. These are computable symmetries which transform any network within an H-equivalence class into another network within that class in a manner that preserves the associated structural invariants. Useful applications of Schützenberger symmetries include enabling the classification and analysis of biological network data, identifying important relationships in social networks, and understanding the consequences of link reconfiguration in communication and sensor networks. View Full-Text
Keywords: Schützenberger symmetry; Schützenberger symmetry group; Green’s relations; network classification; network evolution; network invariants Schützenberger symmetry; Schützenberger symmetry group; Green’s relations; network classification; network evolution; network invariants
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Parks, A.D. Schützenberger Symmetries in Network Structures. Symmetry 2018, 10, 260.

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