No picture for Miyuki, or link from her to Konata, Tsukasa, or Kagami? No direct link from Minami to Yutaka? Either this chart is somewhat misleading, or there is some iteration of Lucky Star very different from the Anime's portrayal.
I'm fairly certain this is a photoshop. The original, printed in the DVD booklets, has no direct link between Kagami and Konata, and in order to add the line Miyuki's face has been removed. Minami and Yutaka are classmates, so the chart is not incorrect.