First off, I'm not big on the extravert/introvert dichotomy, simply because I'm not big on dualistic systems. A spectrum is a much more interesting and accurate way to examine how people "recharge", although that wouldn't be as convenient for cartoonists and self-help gurus who garner 100+ comment threads by caricaturing extroverts as manic monsters and introverts as idiot children. But the example in the above cartoon of introverts giving their energy in social situations made me think: spending your energy on social interactions is not the same thing as contributing energy to social interactions.
Consider: certain types of people suck the energy out of any interaction, whether it's a one-on-one situation or a group setting. They're difficult to talk to, and they're difficult to sit quietly with, because they're needy. This can manifest in various ways, and it's not confined to one side of the spectrum. A loud, dominating personality might try to drag all the energy in the room to himself, requiring people to either throw up shields or be bombarded by an excess of energy that only exhausts; a silent, parasitic personality might constantly absorb energy without giving any back. Interacting with energy sinks is wearing whether you veer toward introversion or extraversion, because there's no way to recharge energy and nowhere to hide.
By way of contrast, let me present to you my brother. He doesn't have to be loud or crazy; he gives energy to any situation he enters just by entering it, whether he's in high spirits or completely, quietly worn out after a long shift. He gives energy to a room even if he's sleeping on the floor at 2 am. He neither sits around waiting for affirmation nor gets up and demands it. He can be boisterous with the loud ones and peaceful with the quiet ones and succinct with the surly ones as needed, but in everything he just is himself, adding life to gatherings large and small, wild or solemn, simply by being there.
Social energy-givers can be active and chatty, or quiet and serene, or anywhere between these two poles. They don't demand an investment of everyone else's energy; they don't requisition attention; they are at ease with themselves and so able to put others at ease. Energy sinks, on the other hand, are often nervous and insecure, whether they're calling attention to themselves with antics or gossip, or trying to influence social perception of themselves by overstated opinions, or desperately trying to fit in, or sullenly begging for bones of affirmation. Some people shift between giving and taking; some are mostly energy-neutral; some are dependably one or the other.
This is not very technical language, of course, but merely my disorganized reactions to the hamster ball analogy of the post above. For a more systematic, virtue-based analysis of what makes a person agreeable society, see Brandon's discussion of affability.
Affability, affabilitas, is also called amicitia, friendliness, but I think that, despite the fact that 'affability' in English usually indicates a matter of temperament rather than character, it is in some ways potentially less misleading. Affability is, roughly, the virtue of making one's interactions with others suitable for friendship; it is not friendship itself, but the acquired disposition of acting outwardly in a way that does not rule friendship out. It is one of those virtues that is widely recognized as a virtue but little discussed, perhaps because it is often classified as a 'lesser virtue', as being very little more than sociable manners taken to a high degree of polish; as we shall see, it is not so clearly minor.