Physics
Journal Club/Seminar
Jose L. Balduz Jr. 
Wednesday,
1/26/2005, 4:30 pm 



The Graph Laplacian as a Tool 

The Laplacian of a graph is
useful in a variety of contexts in and outside of physics, especially when
one has the solutions to the associated eigenproblem. This is illustrated in
a recent paper by F. Y. Wu,
In this paper Wu constructs a
Laplacian matrix from the individual resistor values in a network, then uses
its eigenvalues and eigenvectors to find the effective electrical resistance
from one point to another. We will make a simple analogy to transfer the
paper’s main result to the physically distinct problem of defining a proper
distance between points in a graph of discrete space; this is shown to
satisfy the triangle inequality. Finally we will compare these results to
those of a dynamical method presented in a previous talk (10/13/2004,
“Modeling Space with Simple Graphs”). 
Please join us for
light refreshments at 4:15pm outside WSC 109.