Eigenvalues of Random Power law Graphs

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How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Kronecker Graphs: An Approach to Modeling Networks (2008, background): “While Kronecker products have been studied by the algebraic combinatorics community (see,.g., (Chow, 1997; Imrich, 1998; Imrich and Klavžar, 2000; Hammack, 2009)), the present work is the first to employthis operation in the design of network models to match real data.”
Community Structure in Large Networks: Natural Cluster Sizes and the Absence of Large Well-Defined Clusters (2008, methodology): “Here we work with the random graph model with given expected degrees, as described by Chung and Lu [42, 40, 44, 39, 41, 45, 46, 43].”
The effect of network topology on the spread of epidemics (2005, background): “Theorem 4 from [6] states under mild conditions that, with high probability, the spectral radius of the graph is”
The Spectra of Random Graphs with Given Expected Degrees (2004, background): “This, however, is not true as shown by a counterexample given in [ 10 ].”
DOULION: counting triangles in massive graphs with a coin (2009, background): “We rather have theoretical knowledge on the few top eigenvalues ([23],[9]) or our knowledge is just empirical ([27],[14]).”
Statistical properties of community structure in large social and information networks (2008, methodology): “Eigenvalues of power law graphs have also been studied by Mihail and Papadimitriou [117], Chung, Lu, Vu [43, 44, 45], and Flaxman, Frieze, and Fenner [69].”