Web services composition has drawn a great attention in computing industries to build complex and large systems. However, web services composition modeling has major challenges, including dependency determination, complexity, user requests dependency, handling cycles within a composition, service redundancy and scalability concerns. The service dependency graph (SDG) between services in a repository should be accurate to ensure the quality of composition and the associated user requests' responses. Despite of the crucial importance of accurate dependencies for adequate web services compositions, current modeling approaches do not provide any metric to evaluate the dependency between services for quality estimation. In this paper, the Mutual Information-based Services Dependency (MISD) model is proposed as a graph-based modeling approach, independent to any given user request. It constructs services dependency graphs based on Web Services Mutual Information (WSMI), a proposed modified version of mutual information as the dependency metric, along with other criteria for an accurate, efficient dependency evaluation. It finds the optimum composition representing the structure of the web services composition in a repository rather than the path of given user requests. The experimental dependency analysis emphasizes the efficiency of the generated OC and accuracy of the constructed SDG to be 76% and 86% higher than the state-of-the-art models respectively. The time cost to build the SDG and to find the OC is reduced dramatically up to 99% for different public repositories compared to the state-of-the-art studies as the number of user requests increases.