In an era of Artificial Intelligence (AI), governments around the world are advancing their digital footprints, and using AI to achieving their objectives of effective and efficient public service delivery and citizens engagement. Knowledge Graph (KG), a constituent AI technology, has proven to be the means through which a government can use to manage the complexity of an e-Government instance, and realize its objective. One area in e-Government that KG is used to address, is the challenge of automated composition of web services, where web services are created and maintained by one government department, but is used by another, in an integrated and interoperable manner. Service composition is the combination of two or more web services to create a composite service in order to accomplish a task. In this paper, we present a KG-based approach for automatically composing web services in an e-Government context. Our aim is to advance the e-Government objective of effective and efficient public service delivery and citizens engagement, given a complex e-Government. We focus on creating a Service Dependency Graph (SDG), which captures the semantic relationships between the services, and we further describe the services with QoS characteristics, and then we create a weighted graph based on these two descriptions. We then adapted the Uniform Cost Search algorithm to find the shortest path between a start node and a goal node. We implement our algorithm, and carried-out experiments to obtain execution times, and we compared our results with benchmark results of comparable experimental setup. The difference in execution times of the service composition task is dependent on factors such as the design of the composition model, the complexity of the composition graph, and the hardware and software environments. Our research approach affords us the means to analyze and design our model; and validate and evaluate our work. Our model and the development approach help to achieve the e-Government goals of efficient and effective service delivery and citizens engagement.