SIAM Review
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
A Semidefinite Programming Approach to Optimal-Moment Bounds for Convex Classes of Distributions
Mathematics of Operations Research
Epidemic thresholds in real networks
ACM Transactions on Information and System Security (TISSEC)
IEEE/ACM Transactions on Networking (TON)
On the evolution of user interaction in Facebook
Proceedings of the 2nd ACM workshop on Online social networks
Spectral analysis of stochastic models of large-scale complex dynamical networks
Spectral analysis of stochastic models of large-scale complex dynamical networks
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The eigenvalues of matrices representing the structure of large-scale complex networks present a wide range of applications, fromthe analysis of dynamical processes taking place in the network to spectral techniques aiming to rank the importance of nodes in the network. A common approach to study the relationship between the structure of a network and its eigenvalues is to use synthetic random networks in which structural properties of interest, such as degree distributions, are prescribed. Although very common, synthetic models present two major flaws: 1) These models are only suitable to study a very limited range of structural properties; and 2) they implicitly induce structural properties that are not directly controlled and can deceivingly influence the network eigenvalue spectrum. In this paper, we propose an alternative approach to overcome these limitations. Our approach is not based on synthetic models. Instead, we use algebraic graph theory and convex optimization to study how structural properties influence the spectrum of eigenvalues of the network. Using our approach, we can compute, with low computational overhead, global spectral properties of a network from its local structural properties. We illustrate our approach by studying how structural properties of online social networks influence their eigenvalue spectra.