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.
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