There are definitely many invisible links that are not made apparent in the diagram and there would be links between Chemistry and Medicine for sure, but I don't see Pharmacology really being linked to Chemistry or crafting.
My reasoning for this is, in simple terms, Chemistry is mixing Substance A + Substance B = Substance C and Substance D in a chemical reaction to produce new substances, while Pharmacology is more Drug/Substance A activates/inhibits (interacts with) Receptor/Target B to produce a physical response in the body, but even though this physical response is sometimes mediated by a chemical reaction in the body it's not really about the reaction so much as the macro-effect as a whole through this "interaction/equilibrium relationship",
That's how I view it anyway
There is a branch of Pharmacy though, called Pharmaceutics, which is the science of preparing and manufacturing pharmaceutical/medicinal products, but then this is very much like cooking by adding ingredients that become more than the sum of their individual components.
Ironically this not far from the historical truth as Apothecarists, the precursor to modern Pharmacists were originally grouped with the green grocers as part of their guild and had to fight very hard to be seen as different. The reason they succeeded was because everyone knew what I green grocer did, but no one really had any idea what the hell Apothecary was or entailed being perceived (incorrectly) as almost some mystic art!
And while Medical Specialists/Physicians have always been perceived as different from Pharmacists/Apothecarists, there is actually a common ancestry between General Medical Practitioners and Pharmacists way back when, but they splintered off to focus on the diagnostic side of medicine while Apothecarists focused on the treatment/therapeutic side of it. From there they diverged significantly but still share many similarities.
I am actually working on the Pharmaceutics and Pharmaceutical Manufacturing section for my The Simplified Elyria Medica at the moment, but am a little time poor so am having trouble finishing it.
If it were me, I'd revise the Medicine branch to be more of an interlinked triad between Medicine, Surgery and Pharmacy with a lot of weighted overlap (unequal distribution of shared knowledge and skills) between Medicine and Pharmacy, Medicine and Surgery and Surgery and the local butcher :P hehe