Spectral analysis of virus spreading in random geometric networks

Author

Preciado, Victor M. ; Jadbabaie, Ali

Author_Institution

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

fYear

2009

fDate

15-18 Dec. 2009

Firstpage

4802

Lastpage

4807

Abstract

In this paper, we study the dynamics of a viral spreading process in random geometric graphs (RGG). The spreading of the viral process we consider in this paper is closely related with the eigenvalues of the adjacency matrix of the graph. We deduce new explicit expressions for all the moments of the eigenvalue distribution of the adjacency matrix as a function of the spatial density of nodes and the radius of connection. We apply these expressions to study the behavior of the viral infection in an RGG. Based on our results, we deduce an analytical condition that can be used to design RGG´s in order to tame an initial viral infection. Numerical simulations are in accordance with our analytical predictions.

Keywords

eigenvalues and eigenfunctions; graph theory; graphs; matrix algebra; spectral analysis; adjacency matrix; analytical predictions; eigenvalue distribution; numerical simulation; random geometric graphs; random geometric networks; spatial density; spectral analysis; viral infection; viral spreading process; virus spreading; Complex networks; Computer networks; Computer viruses; Computer worms; Eigenvalues and eigenfunctions; Humans; Large-scale systems; Numerical simulation; Random variables; Spectral analysis;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on

Conference_Location

Shanghai

ISSN

0191-2216

Print_ISBN

978-1-4244-3871-6

Electronic_ISBN

0191-2216

Type

conf

DOI

10.1109/CDC.2009.5400615

Filename

5400615