A Framework for Analyzing the Robustness of Graph Models

Graphs - and sparse matrices - provide a powerful representation for expressing the complex structural relationship between elements in a set, which is why they are used extensively in graph machine learning, network analytics, and scientific computing. One of the challenges in this field is obtaining large scale graph data for performance evaluation. Here, parameterized graph models and their corresponding generators fill in the gap. While there is much work on how well these models represent real data, there are open questions as to how sensitive, or robust, these dials are to noise. In this paper we present a framework for evaluating parameterized graph models in order to study how perturbations to these parameters affect the global structure of the resulting graph. We discuss how this framework is extensible to any graph model and choice of graph features. Further, we provide a case study for Kronecker graphs and analyze the effects of varying the parameters of the Kronecker Graph's initiator matrix, along with injecting noise into the graph on global features. What we will see is that certain features have varying degrees of robustness relative to parameter being modified.