Estrada Index and Laplacian Estrada Index of Random Interdependent Graphs

Yilun Shang
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Yilun Shang: Department of Computer and Information Sciences, Northumbria University, Newcastle NE1 8ST, UK

Mathematics, 2020, vol. 8, issue 7, 1-8

Abstract: Let G be a simple graph of order n . The Estrada index and Laplacian Estrada index of G are defined by E E ( G ) = ∑ i = 1 n e λ i ( A ( G ) ) and L E E ( G ) = ∑ i = 1 n e λ i ( L ( G ) ) , where { λ i ( A ( G ) ) } i = 1 n and { λ i ( L ( G ) ) } i = 1 n are the eigenvalues of its adjacency and Laplacian matrices, respectively. In this paper, we establish almost sure upper bounds and lower bounds for random interdependent graph model, which is fairly general encompassing Erdös-Rényi random graph, random multipartite graph, and even stochastic block model. Our results unravel the non-triviality of interdependent edges between different constituting subgraphs in spectral property of interdependent graphs.

Keywords: Estrada index; Laplacian Estrada index; eigenvalue; random graph (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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