Same Stats, Different Graphs

Data analysts commonly utilize statistics to summarize large datasets. While it is often sufficient to explore only the summary statistics of a dataset (e.g., min/mean/max), Anscombe's Quartet demonstrates how such statistics can be misleading. Graph mining has a similar problem in that graph statistics (e.g., density, connectivity, clustering coefficient)

To find graphs that are identical over a number of graph statistics and yet are different, we use the ground truth data for small non-isomorphic graphs. For larger graphs, we use the graph generators together with some filters.

In fact, we can fix different combinations of 5 statistics and still get multiple distinct graphs. We visualize this with figures that encapsulate the variability of one statistic in 10 slots, covering the ranges [0.0, 0.1], [0.1, 0.2], ... [0.9,1] and in each slot we show a graph (if it exists) drawn by a spring layout;