The present disclosure provides a fast approximate as well as exact hierarchical network storage and retrieval system and method for encoding and indexing graphs or networks as well as for identifying substructure matches or analogs within graph data. Cognitive Memory encodes graphs via generalized combinatorial maps and a new quantum-inspired Q-Hashing algorithm to summarize local structures of the graph along with a contraction and graph property calculation to build an index data structure called the Cognitive Signature for property based, analog based or structure or sub-structure based search. The system and method of the present invention is ideally suited to store and index all or parts or substructures or analogs of graphs as well as dynamically changing graphs such as traffic graphs or flows and motion picture sequences of graphs. The system and method has the advantage that properties of the Cognitive Signature of the graph can be used in correlations to the properties of the underlying data making the system ideal for semantic indexing of massive scale graph data sets.