Graph entropy quantifies uncertainty, characterizing both the efficiency of information extraction and the structural complexity of graphs. For diverse applications, numerous entropy measures have been defined based on distinct graph invariants. Determining the structural properties of minimum-entropy graphs is not only theoretically significant but also highly challenging. In this paper, by investigating two types of edge operations and their inverses, we improve and extend the existing conditions for reducing degree-based graph entropy. Our results provide a basis for developing a strategy to minimize the degree-based graph entropy of connected graphs with fixed numbers of vertices and edges.