On the Eigenvalue Power Law

@incollection{citeulike:1353023, abstract = {We show that the largest eigenvalues of graphs whose highest degrees are Zipf-like distributed with slope \$\alpha\$ are distributed according to a power law with slope \$\alpha /2\$. This follows as a direct and almost certain corollary of the degree power law. Our result has implications for the singular value decomposition method in information retrieval.}, author = {Mihail, Milena and Papadimitriou, Christos }, citeulike-article-id = {1353023}, journal = {Randomization and Approximation Techniques : 6th International Workshop, RANDOM 2002, Cambridge, MA, USA, September 13-15, 2002. Proceedings}, keywords = {eigenvalue, powerlaw}, pages = {953}, posted-at = {2007-05-31 23:40:19}, priority = {2}, title = {On the Eigenvalue Power Law}, url = {http://www.springerlink.com/content/fy1hxala8cqwujh8 }, year = {2002} }

TY - CHAP ID - citeulike:1353023 L3 - citeulike-article-id:1353023 TI - On the Eigenvalue Power Law JF - Randomization and Approximation Techniques : 6th International Workshop, RANDOM 2002, Cambridge, MA, USA, September 13-15, 2002. Proceedings SP - 953 EP - 953 N2 - We show that the largest eigenvalues of graphs whose highest degrees are Zipf-like distributed with slope $\alpha$ are distributed according to a power law with slope $\alpha /2$. This follows as a direct and almost certain corollary of the degree power law. Our result has implications for the singular value decomposition method in information retrieval. KW - eigenvalue KW - powerlaw AU - Mihail, Milena AU - Papadimitriou, Christos PY - 2002/// UR - http://www.springerlink.com/content/fy1hxala8cqwujh8 ER -