A connected graph is a network for which there is a path between any pair of vertices.

A connected graph is graph that is connected in the sense of a topological space, i.e., there is a path from any point to any other point in the graph. A graph that is not connected is said to be disconnected. This definition means that the null graph and singleton graph are considered connected, while empty graphs on n>=2 nodes are disconnected. According to West, the singleton graph K_1, "is annoyingly inconsistent" since it is connected (specifically, 1-connected), but for consistency in discussing connectivity, it is considered to have vertex connectivity κ(K_1) = 0.

algebraic connectivity | biconnected graph | degree sequence | disconnected graph | edge connectivity | Euler transform | k-connected graph | network | planar connected graph | polyhedral graph | polynema | regular graph | Riddell's formula | scale-free network | sequential graph | Steinitz's theorem | Tait's Hamiltonian graph conjecture | vertex connectivity

college level