There are many differenct mechanisms for this, but you should first find out in what layer of your architecture this communication belongs.
One of the purposes of the MVVM framework is that different views can be made over the same viewmodel. Would those usercontrols talk to each other only in the view you are currently implementing, or would they have to talk to each other in other possible views? In the latter case, you want to implement it below the view level, either in the viewmodel or the model itself.
An example of the first case may be if your application is running on a very small display surface. Maybe your user controls have to compete for visual space. If the user clicks one usercontrol to maximize, the others must minimize. This would have nothing to do with the viewmodel, it's just an adaption to the technology.
Or maybe you have different viewmodels with different usercontrols, where things can happen without changing the model. An example of this could be navigation. You have a list of something, and a details pane with fields and command buttons that are connected to the selected item in the list. You may want to unit test the logic of which buttons are enabled for which items. The model isn't concerned with which item you're looking at, only when button commands are pressed, or fields are changed.
The need for this communication may even be in the model itself. Maybe you have denormalized data that are updated because other data are changed. Then the various viewmodels that are in action must change because of ripples of changes in the model.
So, to sum up: "It depends...."