Spectral analysis of dynamically evolving networks with linear preferential attachment

Author

Preciado, Victor M. ; Jadbabaie, Ali

Author_Institution

Dept. of Electr. & Syst. Eng., Univ. of Pennsylvania, Philadelphia, PA, USA

fYear

2009

fDate

Sept. 30 2009-Oct. 2 2009

Firstpage

1293

Lastpage

1299

Abstract

This paper is devoted to study the eigenvalues of the adjacency matrix for the random graph process proposed by Barabasi and Albert in [2]. While many structural characteristics of the Barabasi-Albert (BA) process are well known, analytical results concerning its spectral properties are still an open question. In this paper, we present new results regarding the distribution of eigenvalues of the adjacency matrix associated to this random graph model. In particular, we derive closed-form expressions for the spectral moments of the adjacency matrix and study the evolution of the spectral moments as the network grows. Based on our results, we extract information regarding the evolution of the spectral radius of the adjacency matrix as the network grows.

Keywords

eigenvalues and eigenfunctions; spectral analysis; adjacency matrix; dynamically evolving networks; eigenvalues; linear preferential attachment; spectral analysis; structural characteristics; Closed-form solution; Data mining; Eigenvalues and eigenfunctions; Mathematical model; Moment methods; Spectral analysis; Stochastic processes;

fLanguage

English

Publisher

ieee

Conference_Titel

Communication, Control, and Computing, 2009. Allerton 2009. 47th Annual Allerton Conference on

Conference_Location

Monticello, IL

Print_ISBN

978-1-4244-5870-7

Type

conf

DOI

10.1109/ALLERTON.2009.5394524

Filename

5394524