Hello, I wonder if anyone can help me understand how to use EdgeStyles on a directed graph.

On an un-directed graph I can do the following:

Graph[{1<->2,3 <-> 2,1<->3}, EdgeStyle -> {1<->2-> Directive[Thickness[0.01],Blue], 3 <-> 2 -> Directive[Thickness[0.005],Red], 
1<-> 3 -> Directive[Thickness[0.02],Green]}]

But on a directed graph the following does not work:

Graph[{1->2,3 -> 2,1->3}, EdgeStyle -> {1->2-> Directive[Thickness[0.01],Blue], 3 -> 2 -> Directive[Thickness[0.005],Red], 
1-> 3 ->  Directive[Thickness[0.02],Green]}]

Can someone help me understand what I am missing here?

Thank you, Grey