Use of graph-structured data models is on the rise - in graph databases, in representing biological and healthcare data as well as geographical data. In order to secure graph- structured data, and develop cryptographically secure schemes for graph databases, it is essential to formally define and develop suitable collision resistant one-way hashing schemes and show them they are efficient. The widely used Merkle hash technique is not suitable as it is, because graphs may be directed acyclic ones or cyclic ones. In this paper, we are addressing this problem. Our contributions are: (1) define the practical and formal security model of hashing schemes for graphs, (2) define the formal security model of perfectly secure hashing schemes, (3) describe constructions of hashing and perfectly secure hashing of graphs, and (4) performance results for the constructions. Our constructions use graph traversal techniques, and are highly efficient for hashing, redaction, and verification of hashes graphs. We have implemented the proposed schemes, and our performance analysis on both real and synthetic graph data sets support our claims. Copyright 2014 ACM.