Word Sense Disambiguation (WSD) is the task of automatically choosing the correct meaning of a word in a context. Due to the importance of this task, it is considered as one of the most important and challenging problems in the field of computational linguistics and plays a crucial role in various natural language processing (NLP) applications. In this paper, we present an improved version of a recent unsupervised graph-based word sense disambiguation method considered to be one of the states of the art techniques. Using WordNet as our knowledge-base, we introduce a new method of combining similarity metrics that uses higher order relations between words to assign appropriate weights to each edge in the graph. Furthermore, we propose a new approach for selecting the most appropriate sense of the target word that makes use of the in-degree centrality algorithm and senses of the neighbor words. Experimental results on benchmark datasets Senseval-2 and Senseval-3 shows that the proposed model outperforms all other graph-based methods presented in the literature.