Abstract
In the recently developed theory of isospectral transformations of networks isospectral compressions are performed with respect to some chosen characteristics (attributes) of the network’s nodes (edges). Each isospectral compression (when a certain characteristic is fixed) defines a dynamical system on the space of all networks. It is shown that any orbit of such dynamical system which starts at any finite network (as the initial point of this orbit) converges to an attractor. This attractor is a smaller network where the chosen characteristic has the same value for all nodes (or edges). We demonstrate that isospectral compressions of one and the same network defined by different characteristics of nodes (or edges) may converge to the same as well as to different attractors. It is also shown that a collection of networks may be spectrally equivalent with respect to some network characteristic but nonequivalent with respect to another. These results suggest a new constructive approach which allows us to analyze and compare the topologies of different networks.
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Acknowledgements
This work was partially supported by the NSF grant CCF-BSF 1615407 and the NIH grant 1RO1EBO25022-01. We would like to thank an anonymous referee for numerous useful comments.
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Bunimovich, L., Shu, L. (2018). On Attractors of Isospectral Compressions of Networks. In: Azamov, A., Bunimovich, L., Dzhalilov, A., Zhang, HK. (eds) Differential Equations and Dynamical Systems. USUZCAMP 2017. Springer Proceedings in Mathematics & Statistics, vol 268. Springer, Cham. https://doi.org/10.1007/978-3-030-01476-6_6
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DOI: https://doi.org/10.1007/978-3-030-01476-6_6
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