In graph theory, a Harris graph is defined as an Eulerian, tough, non-Hamiltonian graph.[1][2] Harris graphs were introduced in 2013 when, at the University of Michigan, Harris Spungen conjectured that a tough, Eulerian graph would be sufficient to be Hamiltonian.[3] However, Douglas Shaw disproved this conjecture, discovering a counterexample with an order of 9 and a size of 14.[1] Currently, there are 241,375 known Harris graphs.[2] The minimal Harris graph, the Hirotaka graph, has an order of 7 and a size of 12.[1][2]