We present in this paper a novel approach for as-you-type top-$k$ keyword search over social media. We adopt a natural "network-aware" interpretation for information relevance, by which information produced by users who are closer to the seeker is considered more relevant. In practice, this query model poses new challenges for effectiveness and efficiency in online search, even when a complete query is given as input in one keystroke. This is mainly because it requires a joint exploration of the social space and classic IR indexes such as inverted lists. We describe a memory-efficient and incremental prefix-based retrieval algorithm, which also exhibits an anytime behavior, allowing to output the most likely answer within any chosen running-time limit. We evaluate it through extensive experiments for several applications and search scenarios, including searching for posts in micro-blogging (Twitter and Tumblr), as well as searching for businesses based on reviews in Yelp. They show that our solution is effective in answering real-time as-you-type searches over social media.