It is not even a minor sign. Narcissism: A person who needs to be admired, have an audience, and be continuously in the limelight; because inside there is a total disconnect to any feelings. Therefore, the ego and mind run riot. Narcissists have no filters, because the guilt and common sense and compassion and empathy we all feel around others, especially those we love, is not there.
No heart, no emotions that are normal, is a big warning. They are inside their own minds like a gerbil on a wheel, never content and always looking for more. More fame, more glory, more admiration and, of course, every physical manifestation of wealth they can grasp.
Greed. That is the classic sign. No possible interest in anyone else's welfare as long as they get what they need.
Then there is the malignant narcissist. This is the type that wants revenge on anyone that is not on-board with his agenda of being admired. If you anger a narcissist? Look out. They have nothing but revenge and seeing your hurt. Your pain, in their mind calms them down so they don't feel any pain. Your pain justifies their happiness, even if it is only for a few minutes or a day or a year. They will go for the jugular and not think a thing of it.
I would think narcissism would be more on the opposite side of this. They would want hoards of people admiring them and grovelling at their beauty. They would want people to be green with envy. They would feed on people just being graced by their presence.
The only time they might want to be alone is to look in a mirror where they can admire their god-like awesomeness.
This is only a guess. I am not a doctor nor did I look it up.
Benedict Arnold 