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I will introduce the notion of operator delocalization, to be contrasted with the more conventional notion of operator growth. I will show that even free quantum mechanical systems, once defined on sufficiently connected networks, can exhibit non-trivial delocalization properties. Some preliminary results on the connection between operator delocalization and quantum many-body chaos will be discussed. As an application, I will show that the notion of operator delocalization is at the core of the observed quantum charging advantage of a class of quantum batteries based on SYK-like models.