Comparative analysis of protein networks has proven to be a powerful approach for elucidating network structure and predicting protein function and interaction. A fundamental challenge for the successful application of this approach is to devise an efficient multiple network alignment algorithm. Here we present a novel framework for the problem. At the heart of the framework is a novel representation of multiple networks that is only linear in their size as opposed to current exponential representations. Our alignment algorithm is very efficient, being capable of aligning 10 networks with tens of thousands of proteins each in minutes. We show that our algorithm outperforms previous approaches for the problem, and produces results that are more in line with current biological knowledge.