Apparently, of the non-independent sort: pestering the Norman android with illogic caused the entire population of androids to shut down.
Either the brains are networked but functionally basically all identical, capable of mimicking human thinking when linked but incapable when not; or then Norman has a kingpin brain different from those of the others, and may indeed do all the thinking for all the others; or then all the androids actually run from a powerful external computing source hidden somewhere in Planet Mudd. Although since Norman could operate outside Planet Mudd for great lengths of time, either he has a special brain capable of that, or then the external brain theory should be ditched altogether.
It would seem that having human-shaped artificial bodies is not a big deal at any of the Trek eras (only Archer's crew has failed to show lack of awe in front of androids, as they encountered none), but also that such bodies virtually never contain brains of note. This is why Ruk and Norman stand out of the crowd, the former probably more than the latter (and not just in physical terms!). Certainly by the time of TNG, our heroes are well used to the idea of brainless humans, at least the ones they use for holographic entertainment; physical androids might also be around, but VOY "Prototype" confirms that Data is unique in the category of sentient androids (as far as the knowledgeable B'Elanna Torres can tell).