<p>A newly developed fuzzy structure known as a multidimensional fuzzy graph represents the most advanced fuzzy depiction of graphs, employing multidimensional fuzzy sets to illustrate and define data with uncertainty. A multidimensional fuzzy graph provides a framework that encompasses all necessary properties for depicting complex data. Nonetheless, being a hybrid model with infinite degrees of freedom, the operations in <span>mdfg</span> are particularly intricate. Consequently, the examination of <span>mdfg</span> with distinct characteristics such as vertex (edge) regularity and vertex (edge) irregularity enhances the feasibility of practical applications. This work primarily investigates regularity, irregularity, edge regularity, and its interconnections with operations including direct products, tensor products, unions, and others. The concluding section examines the prospective applications of regular multidimensional fuzzy graphs in relation to the connectivity index, offering appropriate demonstrations and contrasting them with earlier fuzzy models, including <i>m</i>-polar fuzzy sets.</p>