The ShowRootLines property will remove the lines as well as the expansion indicators when set to false. Which is not exactly what you asked for, but maybe it will work for you.

I don't think there is any feasible way to do this. You could theoretically implement the IUIElementCreationFilter interface and remove certain connectors, but the problem lies in knowing which node it belongs to. You might be able to hack it out by comparing its rect to the position of the node's expansion indicator and its text.