How do you search a graph? An interview question I was asked. I was first asked how to traverse a graph and next I was asked how to search one.  Got the first one but not the second. 

What is the modern standard way to search a graph (assume undirected) given no other context? I've a notion that it might have something to do with Dijkstra's algorithm but IDK what. It makes sense that one way is to simply traverse the graph until you find the item you are looking for but it sure doesn't seem optimal.
Interviewer was probably fishing for words like: preorder, inorder, postorder traversal and depth-first versus breadth-first.  I am thinking of traversal as simply having an iterator over the graph that returns some vertices and edges in some particular order.  As Richerby says, you could fill books with all the various ways that this could happen.

As for searching graphs, if they didn't mean traversal; then they probably meant searching for subsets efficiently: If a graph is known to have implicit structure (ie: find all edges in: 192.168.4.0/24 -> 10.0.3.2/24 by hour, etc), then various kinds of searches over src/dst/time are often possible.  Facebook/Twitter, etc are utterly gigantic graphs of "at time T, A says X to B".