ROBUST ALGEBRAIC CONNECTIVITY

I. A. Kuruzov; Курузов И. А.; A. V. Rogozin; Рогозин А. В.; S. A. Chezhegov; Чежегов С. А.; A. B. Kupavskii; Купавский А. Б.

doi:10.31857/S0132347423060067

ROBUST ALGEBRAIC CONNECTIVITY

Authors: Kuruzov I.A.¹^,2, Rogozin A.V.¹, Chezhegov S.A.¹, Kupavskii A.B.¹
Affiliations:
1. Moscow Institute of Physics and Technology
2. Institute for Information Transmission Problems of the RAS (Kharkevich Institute)
Issue: No 6 (2023)
Pages: 49-59
Section: DATA ANALYSIS
URL: https://rjmseer.com/0132-3474/article/view/675729
DOI: https://doi.org/10.31857/S0132347423060067
EDN: https://elibrary.ru/FWLNGZ
ID: 675729

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Abstract

The second smallest eigenvalue of a graph Laplacian is known as algebraic connectivity of the graph. This value shows how much this graph is connected. But this metric does not take into attention possible changes in graph. Note, that deletion of even one node or edge can lead the graph to be disconnected. This work is devoted to development of a metric that should describe robustness of the graph to such changes. All proposed metrics are based on algebraic connectivity. Besides, we provide generalization of some famous optimization methods for our robust modifications of algebraic connectivity. Moreover, this work contains some numerical experiments demonstrated efficiency of proposed approaches.

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