- In classical mechanics, the Hamiltonian is a function describing the state of a mechanical system in terms of position and momentum variables. See Hamiltonian mechanics.
- In quantum mechanics, the Hamiltonian is an operator corresponding to the total energy of a system. See Hamiltonian (quantum mechanics).

In graph theory, a graph is

Both the Hamiltonian operator in physics and Hamiltonian cycles in graph theory are named after Sir William Rowan Hamilton.