The Infinity Mirror Test for Analyzing the Robustness of Graph Generators

Abstract

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 modelling 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.

Growing Better Graphs With Latent-Variable Probabilistic Graph Grammars

“…Current research in graph modelling and graph generation evaluate their results by comparing the generated graphs with the original graph by aggregate properties like degree distribution, clustering coe cients, or diameter [2,3,5,12,13,21]. ere are two potential problems with such metrics.…”

“…For example, in Figure 2, the bag η 2 induces the rule shown at right. e LHS is N 3 because the sepset between η 2 and its parent has three nodes (3,4,5); in the RHS, these three nodes are marked as external. e node numbers are for illustration purposes only; they are not actually stored with the production rules.…”

“…e node numbers are for illustration purposes only; they are not actually stored with the production rules. e RHS has two terminal edges (2-3, 2-4) from the original graph and one nonterminal edge (2)(3)(4)(5) corresponding to the sepset between η 2 and its one child.…”