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 points in a network are related. In contrast, a disconnected graph has at least two vertices that cannot be reached from one another. Connected graphs can be either undirected, where edges have no direction, or directed, where edges point from one vertex to another. The concept of connectedness is fundamental in studying the properties of graphs, such as in König's theorem or MST (Minimum Spanning Tree) algorithms.