 
Summary: EIGENVALUES, EXPANDERS AND SUPERCONCENTRATORS
(Extended Abstract)
Noga Alon* 7 V. D. Milman**
*M.I.T. Cambridge, Massachusetts 02139
AT&T Bell Laboratories, Murray Hill, N J 07974
**Department of Mathematics, Tel Aviv University, Tel Aviv, Israel
ABSTRACT
Explicit construction of families of linear expanders
and superconcentrators is relevant to theoretical computer
science in several ways. There is essentially only one
known explicit construction. Here we show a
correspondence between the eigenvalues of the adjacency
matrix of a graph and its expansion properties, and
combine it with results on Group Representations to
obtain many new examples of families of linear expanders.
We also obtain better expanders than those previously
known and use them to construct explicitly
nsuperconcentrators with =157.4 n edges, much less
than the previous most economical construction.
1. INTRODUCTION
