The following is a few of the more unique graph theory terms which I have misused in the past.

- A
**giant component**is a connected subgraph that contains a majority of the entire graph’s nodes - The
**order**of the graph is the number of vertices, and the**size**is the number of edges. - A
**walk**is an alternating sequence of vertices and edges, beginning and ending with a vertex. A**closed walk**starts and ends son the same vertex. An**open walk**doesn’t. A**trail**is a walk where all the*edges*are distinct. - An
**(open) neighborhood**of a vertex*v*is all the vertices adjacent to*v*, but excluding*v*. A**closed neighborhood**includes*v*. - This one is trivial but I’ve seen it misused often which is can be a big source of confusion. For an edge
*(i,j)*,*i*is the**tail**and*j*is the**head**. I remember that by thinking of the head as the arrowhead. - The
**zweieck**of an undirected edge*e=(u,v)*is the pair of directed edges*(u,v)*and*(v,u)*. It’s a german word that means “biangle”. - An
**orientation**is an assignment of directions to the edges of an undirected graph. A**strong orientation**is an orientation that produces a strongly connected digraph.