This paper investigates how to facilitate users' exploration through data graphs. The prime focus is on knowledge utility, i.e. increasing a user's domain knowledge while exploring a data graph, which is crucial in the vast number of user-facing semantic web applications where the users are not experts in the domain. We introduce a highly unique exploration support mechanism underpinned by the subsumption theory for meaningful learning. A core algorithmic component for operationalising the subsumption theory for meaningful learning is the automatic identification of knowledge anchors in a data graph (KADG). We present several metrics for identifying KADG which are evaluated against familiar concepts in human cognitive structures. The second key component is a subsumption algorithm that utilises KADG for generating exploration paths for knowledge expansion. The implementation of the algorithm is applied in the context of a Semantic data browser in a music domain. The resultant exploration paths are evaluated in a task-driven experimental user study compared to free data graph exploration. The findings show that exploration paths, based on subsumption and using knowledge anchors, lead to significantly higher increase in the users' conceptual knowledge and better usability than free exploration of data graphs. The work opens a new avenue in semantic data exploration which investigates the link between learning and knowledge exploration. We provide the first framework that adopts educational theories to inform data graph exploration for knowledge expansion which extends the value of exploration and enables broader applications of data graphs in systems where the end users are not experts in the specific domain.