# A Study of Regular and Irregular Neutrosophic Graphs with Real Life Applications
## 5 Complete Bipartite Neutrosophic Graphs
### Social Networks  
Social networks are platforms on which millions of people are interconnected everywhere in the world. There are many social networks Ficebook (2007) like Facebook, WhatsApp, and Instagram. These networks have reached a rapid progress in recent years and have spread all over the world in several ways. There are also some security issues pointed out recently by ethical hacking teams; hence to maintain the privacy of the user and the data released by them. In the medium, messages could be tamperedwith easily when a user sends the information to all the other users of his/her group. However, the situation is that a user should be connected to all other users. Social networks can be modeled by a neutrosophic regular graph, since \(d_{m}\)-degree farthest vertices are assumed by paths; therefore, it is a vertex that has at most \(d_{m}\)-degrees; hence, the secrecy of this vertex is maintained, and the user information is secured. If all the vertices of a social network have the same neutrosophic \(d_{m}\)-degree, then the user's secrecy is maintained by adding a lowest arc and producing a \(d_{m}\)-degree in these graphs. Therefore, in these ways, in social networks, the data integrity is maintained, resisting more neighborhood attacks and threats.  
The concept of regularity plays an important role in modeling many real-life optimization problems (e.g., social networks, wireless networks, road networks, assignment problems), so the main focus of this study is to present the concept of regularity in neutrosophic graph theory. The degree of a vertex in a graph is a way to find the number of relations of a vertex, so to analyze a network, it is very essential to find the degree of vertices. In this study, we have described the different types of degrees (\(d_{m}\)-degree and \(td_{m}\)-degree) of nodes in a neutrosophic graph. The idea of the neutrosophic degree of a node is very important from different aspects in the real-world. Here, we have presented the definition of the free vertex (node) and busy vertex (node) of a regular neutrosophic graph, which are very useful to find the solutions of many real-life problems like the traffic congestion problem. Finally, we have mentioned some real-life applications of the regular neutrosophic graph, complete bipartite neutrosophic graph, and node \(d_{m}\)-degree of a neutrosophic graph. This study will be useful when the neutrosophic graphs are extremely large. For example, we have described the utility of the regular neutrosophic graph to model a social network. In the Twenty First Century, social networks are platforms on which millions of people are interconnected everywhere in the world. Therefore, as a future study, we will have to consider some large regular neutrosophic fuzzy graphs to model the social networks in real-life scenarios, and the closeness and diameter need to be computed for the analysis of this social network. Furthermore, we will try to propose some algorithmic methods to determine the closeness and diameter of any social network in real life. Despite the demand for future work, this paper is a useful initial contribution to neutrosophic graph theory, and some problems are described under the neutrosophic environment.