With the advent of the WordNet (a lexical database), the field of linguistics ushered into the new realm where this structured database, based on ontology can be used for a variety of operations such as Word Sense Disambiguation (WSD), checking Semantic Similarity, performing Text Based Summarization etc. The development of various knowledge bases/lexicons like WordNet, with graphically structured information allowed many graph based approaches to be used for choosing the best sense in the Word Sense Disambiguation process. In these graph based approaches, local graph connectivity measures like Fuzzy Degree Centrality ($\mathrm{V}_{\mathrm{F}\mathrm{D}\mathrm{C}}$), Fuzzy Closeness Centrality ($\mathrm{V}_{\mathrm{F}\mathrm{C}\mathrm{C}}$), Fuzzy Betweenness Centrality ($\mathrm{V}_{\mathrm{F}\mathrm{B}\mathrm{C}}$), Fuzzy PageRank Centrality ($\mathrm{V}_{\mathrm{F}\mathrm{P}\mathrm{C}}$) and global graph connectivity measures like Fuzzy Compactness ($\mathrm{V}_{\mathrm{F}\mathrm{C}}$) and Fuzzy Graph Entropy ($\mathrm{V}_{\mathrm{F}\mathrm{G}\mathrm{E}}$) are widely used to perform WSD.Proposed and implemented here is a novel fuzzy graph connectivity measure named as Fuzzy Expected Force (FExF) to choose the correct word sense, by taking into consideration the influential as well as less influential nodes for the node under consideration in the graph formed using Fuzzy Hindi WordNet. FExF performs less computations than $\mathrm{V}_{\mathrm{F}\mathrm{G}\mathrm{E}}$ to give accurate results; thus becoming a reliable local graph connectivity measure, as overall structure of graph is not necessary for finding correct sense of the word.