A connected graph is a type of graph in which there is a path between every pair of vertices. This means that you can start at any vertex and reach any other vertex by traversing the edges of the graph. Connected graphs are important in various fields, including computer science and network theory, as they help in understanding how different components are linked. In contrast, a graph that is not connected is called a disconnected graph. In a disconnected graph, some vertices cannot be reached from others, resulting in isolated subgraphs. Connected graphs can be either undirected, where edges have no direction, or directed, where edges point from one vertex to another, as seen in structures like social networks or transportation systems.