A regular graph is a type of graph in which each vertex has the same number of edges connected to it. This means that every node, or point, in the graph has an equal degree, which is the number of edges incident to it. Regular graphs can be classified based on their degree, such as k-regular graphs, where every vertex has degree k. Regular graphs are important in various fields, including network theory and combinatorics. They help in studying the properties of networks and can be used to model situations where uniform connectivity is required, such as in social networks or transportation systems.