Hamilton road (loop) and Hamilton graph (Hamilton graph) pass through each node of graph G once, and the only path (loop) is Hamilton road (loop). A graph with Hamilton cycles is a Hamilton graph.

In 1960, Ole, an American graph theory mathematician, gave a sufficient condition that a graph is a Hamilton graph: for a graph with more than 2 vertices, if the sum of any two degrees in the graph is greater than or equal to the total number of vertices, then the graph must be a Hamilton graph. A closed Hamilton path is called a Hamilton cycle, and a path containing all vertices in a graph is called a Hamilton path.