  Exploiting recent developments in information theory, we propose, illustrate,
and validate a principled information-theoretic algorithm for module discovery
and resulting measure of network modularity. This measure is an order parameter
(a dimensionless number between 0 and 1). Comparison is made to other
approaches to module-discovery and to quantifying network modularity using
Monte Carlo generated Erdos-like modular networks. Finally, the Network
Information Bottleneck (NIB) algorithm is applied to a number of real world
networks, including the "social" network of coauthors at the APS March Meeting
2004.
