<p>Nowadays in reality there are a lot of uncertainties and it is well-known that fuzzy graphs can efficiently handle such a situation. Picture fuzzy graph is a generalization of fuzzy graph and intuitionistic fuzzy graph. A special type of picture fuzzy graph is regular picture fuzzy graph which has many applications in reality. This article introduces different properties of regular picture fuzzy graph and totally regular picture fuzzy graph. A necessary and sufficient condition regarding equivalence of regular picture fuzzy graph and totally regular picture fuzzy graph has been studied. Beside this, we have introduced some important properties and derived some significant theorems related to regular and totally regular picture fuzzy graph. Furthermore, we present an algorithm along with a flowchart to determine whether a picture fuzzy graph is regular or not. We present a formal proof validating the correctness of the algorithm, along with a flowchart illustrating its steps and an analysis of the algorithm’s time complexity. Finally, using the properties of regular picture fuzzy graph, we proposed an application of social network analysis to determine the key influencer among the social network users. </p>