Description: A quasi-regular graph is a type of graph in which each vertex has a degree that approximates a fixed value, although it is not necessarily equal. This means that, in a quasi-regular graph, the variation in the number of connections (or edges) that each vertex has is minimal, allowing most vertices to maintain a similar degree. This property is useful in various applications, as it allows modeling systems where uniformity in connections is desirable but not strictly necessary. Quasi-regular graphs are a generalization of regular graphs, where all vertices have the same degree. In a quasi-regular graph, some flexibility is allowed, which can be advantageous in situations where a balance between connectivity and diversity of relationships is sought. This characteristic makes them relevant in the study of complex networks, where interactions between nodes may vary slightly, yet a coherent overall structure is still desired. In summary, quasi-regular graphs are a valuable tool in graph theory, providing a framework for analyzing and understanding interconnected systems with controlled degrees of variability.
