Many distributed graph computing systems have been developed recently for efficient processing of massive graphs. These systems require many messages to be exchanged among computing machines at each step of the computation, making communication bandwidth a major performance bottleneck. We present a coded computing framework that systematically injects redundancy in the computation phase to enable coding opportunities in the communication phase thus reducing the communication load substantially. Specifically, we propose coded schemes that enable an inverse-linear trade-off (asymptotically) between computation load and average communication load for Erdös-Rényi (ER) random graph. The proposed scheme for ER graph is shown to be optimal asymptotically as the graph size $n\rightarrow \infty$. For finite $n$, we demonstrate via numerical analysis that for a given computation load $r$, i.e. when each graph vertex is carefully stored at $r$ servers, the proposed scheme slashes the average communication load by (nearly) $r$.