On the second eigenvalue of random regular graphs
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Partitioning sparse matrices with eigenvectors of graphs
SIAM Journal on Matrix Analysis and Applications
A Spectral Technique for Coloring Random 3-Colorable Graphs
SIAM Journal on Computing
Finding a large hidden clique in a random graph
proceedings of the eighth international conference on Random structures and algorithms
On power-law relationships of the Internet topology
Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
Spectral Partitioning of Random Graphs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Spectral techniques applied to sparse random graphs
Random Structures & Algorithms
Finding Planted Partitions in Random Graphs with General Degree Distributions
SIAM Journal on Discrete Mathematics
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We investigate the Laplacian eigenvalues of a random graph G(n,d) with a given expected degree distribution d. The main result is that w.h.p. G(n,d) has a large subgraph core(G(n,d)) such that the spectral gap of the normalized Laplacian of core(G(n,d)) is $\geq1-c_0{\bar d}_{\min}^{-1/2}$ with high probability; here c00 is a constant, and ${\bar d}_{\min}$ signifies the minimum expected degree. This result is of interest in order to extend known spectral heuristics for random regular graphs to graphs with irregular degree distributions, e.g., power laws. The present paper complements the work of Chung, Lu, and Vu [Internet Mathematics 1, 2003].