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Word sense disambiguation (WSD) has been a long-standing research objective for natural language processing. In this paper we are concerned with developing graph-based unsupervised algorithms for alleviating the data requirements for large scale WSD. Under this framework, finding the right sense for a given word amounts to identifying the most "important" node among the set of graph nodes representing its senses. We propose a variety of measures that analyze the connectivity of graph structures, thereby identifying the most relevant word senses. We assess their performance on standard datasets, and show that the best measures perform comparably to state-of-the-art.