Hi everyone!
I downloaded graphviz for mac via macports. The installation was successful because if I type the dot -V command on the terminal, the terminal reports the downloaded version.
But when I try to open a .dot file using the “Open with” option, Graphviz doesn’t appear among the choices. Furthermore, among my applications I only find IDLE and Python Launcher (which I don’t know what they are for). Can someone help me? I’m a little confused 
You need to ask Macports to ask how file associations work.
If I’m not mistaken, and as you apparently discovered, when Graphviz is installed as just a set of shell command line tools, there’s no association of any file types to any interactive programs.
If you can also install the interactive MacOS Graphviz.app with Macports, then possibly the post install actions could create this file association.
Also FYI/FYA a long time ago we realized it was hopeless to ignore Microsoft Word’s appropriation of .dot for “doc template” files, so we started using the.gv suffix instead (anyway .gv is more logical), but I think in MacOS land, a given suffix can have multiple app associations. For now you might have to set this up manually in Finder. Here’s one article about that, from Macrumors.