Abstract: Research on large-scale complex networks has important applications in diverse systems of current interest, including the Internet, the World-Wide Web, social, biological, and chemical networks. The growing availability of massive databases, computing facilities, and reliable data analysis tools has provided a powerful framework to explore structural properties of such real-world networks. However, one cannot efficiently retrieve and store the exact or full topology for many large-scale networks. As an alternative, several stochastic network models have been proposed that attempt to capture essential characteristics of such complex topologies. Network researchers then use these stochastic models to generate topologies similar to the complex network of interest and use these topologies to test, for example, the behavior of dynamical processes in the network such as virus/rumor spreading, distributed consensus, or synchronization of oscillators in a network. In this talk, we review results concerning spectral properties of popular stochastic network models proposed in recent years. In particular, we have developed several methods to determine or estimate the spectral moments of these models. We also present a variety of techniques to extract relevant spectral information from a finite sequence of spectral moments. Our ultimate objective is to use such results to understand and predict the behavior of dynamical processes taking place in large-scale networks.
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