Maximizing algebraic connectivity in interconnected networks

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Show simple item record Shakeri, Heman Albin, Nathan Sahneh, Faryad D. Poggi-Corradini, Pietro Scoglio, Caterina 2016-09-20T17:26:27Z 2016-09-20T17:26:27Z
dc.description Citation: Shakeri, H., Albin, N., Sahneh, F. D., Poggi-Corradini, P., & Scoglio, C. (2016). Maximizing algebraic connectivity in interconnected networks. Physical Review E, 93(3), 6. doi:10.1103/PhysRevE.93.030301
dc.description.abstract Algebraic connectivity, the second eigenvalue of the Laplacian matrix, is a measure of node and link connectivity on networks. When studying interconnected networks it is useful to consider a multiplex model, where the component networks operate together with interlayer links among them. In order to have a well-connected multilayer structure, it is necessary to optimally design these interlayer links considering realistic constraints. In this work, we solve the problem of finding an optimal weight distribution for one-to-one interlayer links under budget constraint. We show that for the special multiplex configurations with identical layers, the uniform weight distribution is always optimal. On the other hand, when the two layers are arbitrary, increasing the budget reveals the existence of two different regimes. Up to a certain threshold budget, the second eigenvalue of the supra-Laplacian is simple, the optimal weight distribution is uniform, and the Fiedler vector is constant on each layer. Increasing the budget past the threshold, the optimal weight distribution can be nonuniform. The interesting consequence of this result is that there is no need to solve the optimization problem when the available budget is less than the threshold, which can be easily found analytically.
dc.rights ©2016 American Physical Society
dc.subject Interdependent Networks
dc.subject Graphs
dc.subject Physics
dc.title Maximizing algebraic connectivity in interconnected networks
dc.type Article 2016
dc.citation.doi 10.1103/PhysRevE.93.030301
dc.citation.issn 1539-3755
dc.citation.issue 3
dc.citation.jtitle Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
dc.citation.spage 6
dc.citation.volume 93
dc.contributor.authoreid faryad
dc.contributor.authoreid albin
dc.contributor.authoreid pietro
dc.contributor.authoreid caterina

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