What type of graph is this? 
My choices are: 
a) A small graph
b) A directed graph
c) A connected graph
d) An unbalanced graph
e) None of the above

Now I know this isn't a small graph or unbalanced graph (I don't even think those are real things) and this is certainly not a directed graph since the edges are not showing a direction, which leaves me with either c or e. 
Is this a trick question? I would think that this is a weighted graph, so the answer would be e: None of the above. However, a undirected graph can be considered 'connected' if there is a edge between every pair of nodes, which in this case is true. If my understanding there is correct, then the answer would be c, would it not? Thanks for any help.

It is indeed connected. Note that a connected graph need not have an edge between every two distinct vertices: it need only have a path. Thus, the graph below is connected even though it has no edge between vertices $1$ and $4$ or between vertices $2$ and $3$.
  1----2  
  |    |  
  3----4

A graph with every possible edge between distinct vertices is a complete graph.
