Before revision:  On the other hand, in many applications, non-graph observations (  side information) exist beside a given graph realization . The non-graph observations are usually independent of the graph structure.
After revision:  On the other hand, in many applications, non-graph observations ( side information) that exists beside a graph realization in many applications. Indeed, the extracted side information can be replaced by a sequence of side information that is independent of the graph structure.