Packages that interface with programming languages and environments:
Matlab BGL (by David Gleich). I will use this for many in-class demos.
Note: if you use a Mac, try the distribution found here
SNAP (by Jure Leskovec). Libraries for C++
NetworkX. A Python package for manipulating and analyzing graphs.
igraph. Can be used in R, C, Python, or Ruby.
JUNG. Is a network analysis package for Java
Stand-alone graph analysis packages:
Linear algebra packages for various languages:
Java: netlib-java, matrix-toolkits-java, Apache Commons Math
Python: Scipy sparse linalg
C or C++ : TAUCS (sometimes hard to install), PETSc, not sure what else