I started using Mathematica a few days ago and came across a problem which I would like to get some help with. I import an image to Mathematica, and after thinning it I convert it to graph using the MorphologicalGraph function. My problem is that when two lines cross each other there should obviously be only one junction, but on the graph there is two, so the software basically breaks the edges up. This effect is certainly enhanced when the angle between the lines deviates from 90degrees. I realize that the thinned image already shows that the lines break up but since I have tried so many things (e.g. having an imput image with thinner lines) and nothing worked, I thought I would ask you All, hoping you can help me. Is there any way I could eliminate these additional vertices? Any help is much appreciated!!