Square doesn't have a network effect, it doesn't really matter if one store uses square, and the neighboring store uses google wallet, dwolla, or something else.
Square and payment systems in general most certainly do have network effects. For instance, I don't have a Discover card because it's not worth the hassle of checking whether each merchant accepts it.
Network effects are the lion's share of the justification behind Square's Starbucks deal.
Yes it does. If their mobile payment app becomes the de facto standard, not accepting payment from that app could become as bad as not accepting credit cards.
Network effects are the lion's share of the justification behind Square's Starbucks deal.