A complement graph is formed from a given graph by reversing its edges. In a complement graph, two vertices are connected by an edge if and only if they are not connected by an edge in the original graph. This means that if a pair of vertices has an edge in the original graph, it will not have an edge in the complement graph, and vice versa. Complement graphs are useful in various fields, including graph theory and network analysis. They help in understanding the relationships between vertices and can be applied in problems involving social networks and computer science, where analyzing connections and disconnections is essential.