graph theory

Question

How many distinct paths of length 4 that do not visit the same node more than once are there between node 0 and node 1?

Answer 1

You should redraw the above figure as 3D diamond. I have tried to draw fairly :P

OR better diagram is this:

I have indicated lower half of the diamond by greeen edges and upper half by black edges and middle 2D plane by red edges.

Now, you need to go to middle 2D plane in 4C1 ways.

Then traverse 2 edges there in 3C1 * 2C1 ways . 

Note: The middle 2D plane is a complete graph.

At last, you can go up to 1 in only 1 way.

So, total = 4*3*2*1 = 4! = 24 ways