Sum of degrees
2 × number of arcs
Walk
Route along edges between two vertices
Path
A route along edges where no vertex is visited more than once
Trail
A walk where no edge is visited more than once.
Cycle
Starts and ends at the same vertex, no other vertex is visited more than once.
Hamiltonian cycle
A cycle that used every vertex
Connected graph
Path between every pair of vertices
Simple graphs
No loops or multiple edges
Directed graph (digraph)
Some/all edges have directions
Complete graph
All vertices are directly connected
Isomorphic graphs
Same graph drawn differently
Planar graph
Can be drawn so no arcs cross
Network/weighted graph
Each edge has a weight
Eulerian
All vertices have even order
Semi-eulerian
Two vertices have odd order
Non-eulerian
More than two vertices have odd order
Minimum spanning tree
Connected graph with no cycles of least total weight
Spanning tree
Subgraph of a graph containing all vertices and is also a tree
