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Data analysts commonly utilize statistics to summarize large datasets. Whileit is often sufficient to explore only the summary statistics of a dataset(e.g., min/mean/max), Anscombe's Quartet demonstrates how such statistics canbe misleading. Graph mining has a similar problem in that graph statistics(e.g., density, connectivity, clustering coefficient) may not capture all ofthe critical properties of a given graph. To study the relationships betweendifferent graph properties and statistics, we examine all low-order (<= 10)non-isomorphic graphs and provide a simple visual analytics system to explorecorrelations across multiple graph properties. However, for graphs with morethan ten nodes, generating the entire space of graphs becomes quicklyintractable. We use different random graph generation methods to further lookinto the distribution of graph statistics for higher order graphs andinvestigate the impact of various sampling methodologies. We also describe amethod for generating many graphs that are identical over a number of graphproperties and statistics yet are clearly different and identifiably distinct.

Same Stats, Different Graphs (Graph Statistics and Why We Need Graph Drawings)