Reproducing Network Structure: A Comparative Study of Random Graph Generators

The problem of generating graphs similar to a given one arises in such tasks as data anonymization and significance testing of network mining tools. Main challenges lie in a rich diversity of graph domains emerging in various research areas and the uncertainty about graph properties to be reproduced. Our central statement is that a good graph generation model should follow two requirements on generated graphs: 1) similarity to the original one in terms of manifold graph metrics, and 2) variability wide enough to mimic natural diversity across a graph domain. In this work we have compared three state-of-the-art graph generators, Embedding based Random Graph Generator, Gscaler, and Stochastic Kronecker Graph, universal enough to fit an arbitrary graph. We found that ERGG and Gscaler greatly outperform SKG in graph reproducing accuracy in terms of graph metrics. An experiment with domain imitation showed that the variability of ERGG generated graphs resembled the original variability, while Gscaler graphs were almost identical.