Post that says partial correlation != conditional dependence/independence: https://www.quora.com/Does-a-partial-correlation-of-0-imply-conditional-independence
Post above points to following paper: https://onlinelibrary.wiley.com/doi/epdf/10.1111/j.1467-842X.2004.00360.x
Post that says GGMs measure partial correlation structure of data, which is a "measure of independence" between variables: http://www.strimmerlab.org/notes/ggm.html
Do you see how I am now confused? Can someone clarify for me?