SPECTRA OF LAPLACIAN MATRICES OF WEIGHTED GRAPHS: STRUCTURAL GENERICITY PROPERTIES

Autor(es)

Poignard, Camille ^[1] ; Pereira, Tiago ^[1] ; Pade, Jan Philipp ^[2]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, ICMC Sao Carlos, BR-13566 Sao Paulo - Brazil

^[2] Humboldt Univ, Dept Math, D-10099 Berlin - Germany

• Tipo de documento: Artigo Científico
• Fonte: SIAM JOURNAL ON APPLIED MATHEMATICS; v. 78, n. 1, p. 372-394, 2018.
• Citações Web of Science: 5

Resumo

This article deals with the spectra of Laplacians of weighted graphs. In this context, two objects are of fundamental importance for the dynamics of complex networks: the second eigenvalue of such a spectrum (called the algebraic connectivity) and its associated eigenvector (the so-called Fiedler vector). Here we prove that, given a Laplacian matrix, it is possible to perturb the weights of the existing edges in the underlying graph in order to obtain simple eigenvalues and a Fiedler vector composed of only nonzero entries. These structural genericity properties with the constraint of not adding edges in the underlying graph are stronger than the classical ones, for which arbitrary structural perturbations are allowed. These results open the opportunity to understand the impact of structural changes on the dynamics of complex systems. (AU)

• Processo FAPESP: 13/07375-0 - CeMEAI - Centro de Ciências Matemáticas Aplicadas à Indústria
• Beneficiário: Francisco Louzada Neto
• Modalidade de apoio: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs