A PhD is already a commitment of years, so choosing the department label on the diploma feels like a strange thing to stress over. Yet that is exactly the question this researcher is asking, and it is a fair one. The core of the dilemma is whether the words "Computer Science" or "Electrical Engineering" on a degree will change how an ATS scanner or a hiring manager sees a Graph ML profile. The research itself stays identical. The branding does not. This is not a trivial concern, but it also risks being a distraction from what actually moves the needle in a research scientist search.
The honest take is that the department name matters far less than the work you produce and the people who vouch for it. Big tech research divisions are not known for hiring based on the department printed on a CV. They look at papers, at the novelty of the methods, at the clarity of the thinking, and at whether you can articulate the impact of your work to a room of skeptical scientists. If your Graph ML research sits in the EECS overlap, you are already in the right neighborhood. The signal that will carry you through ATS filters is not "CS" versus "EE"; it is the specific keywords in your project descriptions, the venues you publish in, and the recommendation letters from advisors who are themselves recognized in the field. This is where the practical advice diverges from the anxiety expressed in the question. Spending energy on which department code appears on a transcript is a zero-sum game with the time you could spend on research quality.
That said, there is a real consideration about flexibility. CS degrees tend to signal broader software engineering competence, which can open doors beyond research into applied roles if the academic job market tightens. EE, on the other hand, carries a signal of signal processing and hardware-adjacent depth, which is increasingly relevant for graph signal processing work. Neither is a wrong choice. Both are respected. The question is whether you want to optimize for perceived breadth or perceived depth, and neither should override the actual substance of your dissertation. If you are worried about saturation, note that the market for AI researchers is not saturated at the top end. It is saturated with candidates who have generic deep learning projects. It is not saturated with people who can connect graph theory, signal processing, and learning in novel ways. That is your edge, regardless of the department.
The practical recommendation is to stop treating this as a branding exercise and start treating it as a research strategy exercise. Talk to your advisor about which department has stronger faculty overlap with your intended methods. Look at where recent graduates from each department ended up, and ask if that trajectory matches your goal. If both paths are equally viable, pick the one that makes your day-to-day life easier, because PhD stress is already high without adding administrative regret. The market in five years will not care about the letters on your degree as much as it cares about the problems you solved. The takeaway worth quoting is this: your department is a label, but your publication record is the proof. If you want to be a research scientist, optimize for the latter.