Simple Path 
Sequence of connected edges with distinct vertices 
X 
X 


Cycle (or circuit) 
Simple path with v1 = vk; all cycles are tours 
X 
X 
X 



Walk 
any sequence of connected edges: $\{v_1, v_2\}, \{v_2, v_3\}, \{v_3, v_4\}\ldots$ 





Tour 
walk that starts and ends at same node 
X 

X 


Eulerian Walk 
connected and at most two odd degree vertices 
X 


X 

Eulerian Tour 
iff connected and every vertex has even degree (allows isolated vertices) 
X 

X 
X 

Hamiltonian Walk 
contains V1 edges 
X 
X 


X 
Hamiltonian Tour 
all hypercubes have one, contains V edges 
X 
X 
X 

X 