Construct an algorithm which determines whether graph is connected or not I've been trying to find a good way of explaining to layperson (who has not taken graph theory) how this algorithm works and I need some help.  
Assume that I have a list of edges in a graph and for instance in edge i we are given node numbers f(i) and g(i).  How do I explain an algorithm to decide whether or not it is connected without going too deep into graph theory language. Please don't put any breadth/depth, transversal, etc...
Basically the person I'm explaining it to only knows that an incidence matrix can be constructed out of a combination of 1, -1, and 0 and understands the definition of connectedness. Additionally I want to convey to him towards the end that when a graph reaches a certain condition it is connected and if the opposite condition its not connected.  
If anyone can give me some help that would be great.  
 A: Imagine a maze with $n$ rooms and a single entrance/exit, where each room contains a gold coin and rooms are connected together via doors. We want to decide whether or not the maze is connected; that is, we want to decide whether or not it's possible to visit every room in the maze and collect all $n$ coins. It's easy to get lost though; fortunately, we also have some red paint and a marker to help us keep track of things. After entering the maze via the only entrance, here's what we'll do:
Every time we enter an unpainted room via some door, we label the door with the word "previous", then do one of three things:


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*If the room has a gold coin, then this is the first time we've entered the room. We pick up the coin, arbitrarily number the $k$ unpainted neighbouring rooms from $1$ to $k$ (excluding the previous room that we just came from), then enter the first neighbouring room.

*If the room has no gold coin but isn't painted, then we must have visited it before and we are simply returning from our trip. We cross off the room we just came from.

*

*If we haven't yet crossed off all of the current room's neighbouring rooms, then we enter the next neighbouring room in the ordering that hasn't yet been crossed off.

*If we've already crossed off all the numbered neighbouring rooms, then we paint the current room red and exit the room via the door labeled "previous".



Eventually, we'll exit the entire maze. When this happens, we count the number of collected gold coins. If we have $n$ coins, then we must have visited every room in the maze, and so it must be connected. Otherwise, some of the rooms in the maze still have their gold coins, and so the maze must be disconnected.
