We introduce the infinity mirror test for the analysis of graph generator performance and robustness when working with empirical networks.
Graph generators learn a model from a source graph in order to generate a new graph that has many of the same properties. The learned models each have implicit and explicit biases built in, and its important to understand the assumptions that are made when generating a new graph. Of course, the differences between the new graph and the original graph, as compared by any number of graph properties, are important indicators of the biases inherent in any modeling task. But these critical differences are subtle and not immediately apparent using standard performance metrics. Therefore, we introduce the infinity mirror test for the analysis of graph generator performance and robustness. This stress test operates by repeatedly, recursively fitting a model to itself. A perfect graph generator would have no deviation from the original or ideal graph, however the implicit biases and assumptions that are cooked into the various models are exaggerated by the infinity mirror test allowing for new insights that were not available before. We show, via hundreds of experiments on 6 real world graphs, that several common graph generators do degenerate in interesting and informative ways. We believe that the observed degenerative patterns are clues to future development of better graph models.
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