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COMBINATORICS
2004
97views more  COMBINATORICS 2004»
13 years 6 months ago
Tight Estimates for Eigenvalues of Regular Graphs
It is shown that if a d-regular graph contains s vertices so that the distance between any pair is at least 4k, then its adjacency matrix has at least s eigenvalues which are at l...
Alon Nilli
PAKDD
2011
ACM
209views Data Mining» more  PAKDD 2011»
12 years 9 months ago
Spectral Analysis for Billion-Scale Graphs: Discoveries and Implementation
Abstract. Given a graph with billions of nodes and edges, how can we find patterns and anomalies? Are there nodes that participate in too many or too few triangles? Are there clos...
U. Kang, Brendan Meeder, Christos Faloutsos
COMBINATORICS
2006
169views more  COMBINATORICS 2006»
13 years 6 months ago
The Diameter and Laplacian Eigenvalues of Directed Graphs
For undirected graphs it has been known for some time that one can bound the diameter using the eigenvalues. In this note we give a similar result for the diameter of strongly con...
Fan R. K. Chung
STOC
2004
ACM
73views Algorithms» more  STOC 2004»
14 years 7 months ago
Spectral partitioning, eigenvalue bounds, and circle packings for graphs of bounded genus
In this paper, we address two longstanding questions about finding good separators in graphs of bounded genus and degree:
Jonathan A. Kelner
DM
1999
89views more  DM 1999»
13 years 6 months ago
On the distribution of eigenvalues of graphs
Let G be a simple graph with n( 2) vertices, and i(G) be the ith largest eigenvalue of G. In this paper we obtain the following: If 3(G) < 0, and there exists some index k, 2 ...
Alexander K. Kelmans, Xuerong Yong