The modular modeling paradigm facilitates the efficient building, verification and handling of complex system models by assembling them from general-purpose component models. A drawback of this paradigm, however, is that the assembled system models may have excessively complex structures for certain purposes due to the amount of detail of the component models, which is introduced to promote modularity. This work presents a domain-independent structural simplification technique that can detect such unnecessary complexities in a modular bond-graph model and eliminate them from the model without compromising accuracy. To this end, the activity concept in the literature is extended to define "inactivity" for junction elements, and simplification is obtained by detecting and eliminating inactive junction elements and by propagating the implications. It is shown that this simple idea can result in models that are conceptually and computationally more efficient. Some subtleties associated with this approach are highlighted.