Social media have great potential to support diverse information sharing, but there is widespread concern that platforms like Twitter do not result in communication between those who hold contradictory viewpoints. Because users can choose whom to follow, prior research suggests that social media users exist in echo chambers or become polarized. We seek evidence of this in a complete cross section of hyperlinks posted on Twitter, using previously validated measures of the political slant of news sources to study information diversity. Contrary to prediction, we find that the average account posts links to more politically moderate news sources than the ones they receive in their own feed. However, members of a tiny network core do exhibit cross-sectional evidence of polarization and are responsible for the majority of tweets received overall due to their popularity and activity, which could explain the widespread perception of polarization on social media.