Math Help - 4 numbered balls placed in 4 sites, two of one kind, and one of another.

Hi. The thing is that I was trying to find the number of graphs with the same topological structure. I was considering a particular graph, of 4 particles, connected by three lines, the first one in the picture. Because the book says so, I know there are 12 ways of ordering those particles with the same topological structure (look at the attached picture). Now, I was trying to make the counting in a statistical ground. I have four particles, wich I can put in four different places, but those places are not all equal. Some connects to two other particles, and some only connects to one particle.



Can somebody help me to do the counting?

Thanks in advance.