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Low-Order Spectral Analysis of the Kirchhoff Matrix for a Probabilistic Graph With a Prescribed Expected Degree Sequence

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2 Author(s)
Victor M. Preciado ; Dept. of Electr. & Syst. Eng., Univ. of Pennsylvania, Philadelphia, PA ; George C. Verghese

We study the eigenvalue distribution of the Kirchhoff matrix of a large-scale probabilistic network with a prescribed expected degree sequence. This spectrum plays a key role in many dynamical and structural network problems such as synchronization of a network of oscillators. We introduce analytical expressions for the first three moments of the eigenvalue distribution of the Kirchhoff matrix, as well as a probabilistic asymptotic analysis of these moments for a graph with a prescribed expected degree sequence. These results are applied to the analysis of synchronization in a large-scale probabilistic network of oscillators.

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IEEE Transactions on Circuits and Systems I: Regular Papers  (Volume:56 ,  Issue: 6 )