A graph G is Hamilton-connected if every two vertices of G are connected by a Hamiltonian path. In other words, a graph is Hamilton-connected if it has a u - v Hamiltonian path for all pairs of vertices u and v. The illustration above shows a set of Hamiltonian paths that make the wheel graph W_5 hamilton-connected. By definition, a graph with vertex count n having a detour matrix whose off-diagonal elements are all equal to n - 1 is Hamilton-connected. Conversely, any graph having a detour matrix with an off-diagonal element less than n - 1 is not Hamilton-connected.

detour matrix | Hamiltonian graph | Hamiltonian path | Hamilton-laceable graph | H^*-connected graph | hypotraceable graph | maximally nonhamiltonian graph | traceable graph