[Fall 1998
Colloquiums]
[Department Homepage]
DEPARTMENT OF MATHEMATICS AND STATISTICS
OAKLAND UNIVERSITY
ROCHESTER, MICHIGAN 48309
Steve Kirkland
Department of Mathematics and Statistics
University of Regina
Algebraic Connectivity, Fiedler Vectors,
and Perron Components for Graphs
Abstract
Given a connected undirected graph G, its Laplacian matrix L is given by L = D A, where A is the adjacency matrix of G and D is the diagonal matrix of vertex degrees. The smallest positive eigenvalue of L is known as the algebraic connectivity of G, while the corresponding eigenvectors are called Fiedler vectors. Some remarkable work of Fiedler describes how both the algebraic connectivity and the Fiedler vectors are influenced by the shape of G. In this talk, we will discuss an approach to this topic which makes use of certain entrywise positive matrices associated with G. In particular, we will describe how techniques from the theory of positive matrices can be exploited to yield new information concerning both the algebraic connectivity of a graph and the associated Fiedler vectors.
372 Science and Engineering Building
Thursday, November 12, 1998
3:004:00 P.M.
Refreshments at 2:303:00 P.M. in Room 368, Science and Engineering Building