If I am Your Friend are you mine?

    - Undirected: (x,y) implies (y,x).            "had sex with"
    - Directed: (x,y) doesn't imply (y,x).      "heard of"

Am I my own friend?

    - loop: (x,x)
    - multiedges: multiple occurrences of (x,y)

    - simple graph: no loops or multiedges

How close of a friend are we?

    - weighted graph: each edge has an associated numerical
        attribute.

                        0 - means enemies
                        10 - means blood brothers
 
Am I linked by some chain of friends to a star?

    - path: a sequence of edges from one vertex to another

            Brian-Fred-Ted-Luthor-Guadalupe-Hulk Hogan

How close is my link to that star?

    - shortest path
 

Is there a path of friends between every two people in the world?

    - connected graph: there is a path between any two vertices

    - strongly connected graph: there is a directed path between
        any two vertices.

    - isolated vertex: a vertex not connected with any other

    - connected component: a vertex in an unconnected graph that
        is connected.

Who has the most friends? The fewest friends?

    - degree of a vertex: the number of edges adjacent to it

    - dense graphs: the vertexes have relatively high degrees

    - sparse graphs: the graphs have low degrees

    - regular graphs: each vertex has the same degree

What is the largest clique?

    - clique: in a sub graph, each vertex pair has an edge between
        them

How long will it take for my gossip to get back to me?

    - cycle:  a path where the last vertex is adjacent to the first

    - simple cycle: no vertex is repeated

    - girth: the shortest cycle in the graph

    - Hamiltonian Cycle: a cycle that traverses every vertex once

 {   - tree: an undirected graph with no cycles

    - directed acyclic graph: directed graph with no directed cycles