• Graph (another word for "network")
• Path (Note that in CS-103 we require each vertex in a "path" to be distinct. For extra clarity on this point, some texts use the term simple path.
• Distance
• Neighborhood
• Cycle
• Acyclic graph
• Tree (part of a Forest)
• Connected Graph (and Connected Component)
• Broadcast Search (more popularly known as Breadth-First Search)

Note that a graph is an ordered pair of two sets: vertices and edges. When we talk about a graph, we usually call it G and refer to the set of vertices as V and the set of edges as E. This all comes together in the statement: G=(V,E)

Here is more about sets:

• Set
• Cardinality (another word for size of a set)
• Intersection of two sets
• Union of two sets
• Partition of a set

And finally, a bit of explanation about ordered vs unordered pairs:

• Ordered pair is written with parenthesis (A,B) and is how mathematicians describe a collection of two elements when it matters which is first and which is second. For example, who is first in line and who is second in line.
• __Unordered pair__ is written with curly braces {A,B} and is how mathematicians describe a collection of two elements when it does not matter which is first and which is second. For example, two people who join the same small group discussion are linked but not distinguished by "first" and "second." An unordered pair is the same thing as a set of size two.