Are Alexander Skarsgård and Ellen Page a thing?

Alexander Skarsgård and Ellen Page were in San Francisco yesterday to attend some Q&A events for their recently released movie The East. During some downtime their director, Zal Batmanglij (brother of Vampire Weekend's Rostam Batmanglij) snapped this cute picture of the twosome and put it on Twitter. So are these two just close co-stars, or more? (lol I think the answer is obvious to anyone who has ever been on L Chat)

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FWIW I was at one of the screenings last night and they definitely gave off the "just great friends" vibe more than anything else. They are both SO nice and ASkars and is actually super funny. The movie isn't perfect but it's still really good and more thought-provoking than 90% of other stuff in theaters right now.