Hamilton Cycle or Euler Circuit

We begin by defining a closed walk, then we analyze the characteristics of four types of closed walks, circuits, Euler Circuits, directed cycles, and Hamilton Cycles (aka Hamilton Circuits). Then we compare the characteristisc of Euler Circuits and Hamilton Cycles. The five characteristics of a walk that is both an Euler Circuit and a Hamilton Cycle are to be closed, have no repeated vertices, no repeated edges, to visit all of the edges, and to visit all of the vertices. A walk that does not visit all of the edges but has the other four characteristics is a Hamilton Circuit. A walk that repeats vertices but has the other four characteristics is a Hamilton Circuit but not an Euler Circuit.