Complexity Aspects of Unstructured Sparse Graph Representation

In this paper, we address the problem of the trade-off between the compact memory representation of graphs and their amount of randomness. We design a representation (abbreviated as DBP representation) which does not use information on the structure of graphs, hence it is generally usable. Based on our theoretical lower bound on graph space representation, we define a compression ratio for a given graph with respect to the DBP representation. Based on experimental results, we derive the empirical relationship between the amount of randomness and the compression ratio.