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In this paper, we study the dynamics of a viral spreading process in randomgeometric graphs (RGG). The spreading of the viral process we consider in thispaper is closely related with the eigenvalues of the adjacency matrix of thegraph. We deduce new explicit expressions for all the moments of the eigenvaluedistribution of the adjacency matrix as a function of the spatial density ofnodes and the radius of connection. We apply these expressions to study thebehavior of the viral infection in an RGG. Based on our results, we deduce ananalytical condition that can be used to design RGG's in order to tame aninitial viral infection. Numerical simulations are in accordance with ouranalytical predictions.

Spectral Analysis of Virus Spreading in Random Geometric Networks