If this is still a problem, then there are several ways depending on what your points look like. You might use edge linking, morphological closing or dilation, imline(), or other methods. Post your image for more advice.
You're a man of very few words. What about the branching points? They are connected to some of the other branching points, but not ALL other branching points (which doesn't seem like you'd want that anyway). Please attach an image showing the binary image that you want for an output.
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