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In this work, we continue the study of a new class of codes, called codes over graphs Here we consider storage systems where the information is stored on the edges of a complete directed graph with n nodes. The failure model we consider is of node failures which are erasures of all edges, both incoming and outgoing, connected to the failed node. It is said that a code over graphs is a \rho-node-erasure-correcting code if it can correct the failure of any \rho nodes in the graphs of the code O(n^2), our main goal in the paper is the construction of codes over smaller fields. In particular, our main result is the construction of optimal binary codes over graphs which correct two node failures with a prime number of nodes.