Hi there, I successfully constructed a gene coexpression network using the package WGCNA. Everything is okay. But right now, I want to get a deeper understanding of the output of this tool. Specifically, When I received a output something like:

As you can see, there are lot of branches with different heights. So what the difference between a longer branch's height [red rectangle] and a shorter branch's height [purple rectangle] ? And is it normal or not that dendrogram height can above 1? thank in advance!

The interpretation of the dendrogram height isn't specific to WGCNA. This is also a general statistics question that you could answer with a simple Google search.

At the risk of sounding like a pompous fool (pompous because I'm promoting my own video, and fool, well...), here's a lecture I gave on module identification from hierarchical clustering. It explains, among other things, what the height means.