This work weakens well-known consistency models using graphs that capture applications' characteristics. The weakened models not only respect application semantic, but also yield a performance benefit. We introduce a notion of dependency graphs, which specify relations between events that are important with respect to application semantic, and then weaken traditional consistency models (e.g., causal consistency) using these graphs. Particularly, we consider two types of graphs: intra-process and inter-process dependency graphs, where intra-process dependency graphs specify how events in a single process are related, and inter-process dependency graphs specify how events across multiple processes are related. Then, based on these two types of graphs, we define new consistency model, namely {\em application-aware} consistency. We also discuss why such application-aware consistency can be useful in social network applications. This is a work in progress, and we present early ideas regarding application-aware consistency here.