Find trending topics and pages from social networks

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Goal

By looking at a user's social network, how can we find trending pages and topics that might be relevant for the user?

Instead of presenting a list of just all the most recently links that appear on a user's home timeline, can we do a better job and pick things that are trending or that are being retweeted/shared more often?

Quality

Can we provide the user with links that are relevant?

Performance

Can we have very recent results ready at any time?

Infrastructure

What do we need to build to do this? How would it scale?