Same Stats, Different Graphs (Graph Statistics and Why We Need Graph Drawings)
arXiv:1808.09913
Abstract
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) may not capture all of the critical properties of a given graph. To study the relationships between different graph properties and statistics, we examine all low-order (<= 10) non-isomorphic graphs and provide a simple visual analytics system to explore correlations across multiple graph properties. However, for graphs with more than ten nodes, generating the entire space of graphs becomes quickly intractable. We use different random graph generation methods to further look into the distribution of graph statistics for higher order graphs and investigate the impact of various sampling methodologies. We also describe a method for generating many graphs that are identical over a number of graph properties and statistics yet are clearly different and identifiably distinct.
arXiv commentAppears in the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018)
References in corpus (15)
- Emergence of scaling in random networks
- Statistical mechanics of complex networks
- The structure and function of complex networks
- Community structure in social and biological networks
- Assortative mixing in networks
- The diameter of the world wide web
- Mixing patterns in networks
- Self-similar community structure in organisations
- Structure of Growing Networks: Exact Solution of the Barabasi--Albert's Model
- Scaling and percolation in the small-world network model
- Scale-free topology of e-mail networks
- Small-world properties of the Indian Railway network
- Epidemic spreading in correlated complex networks
- Pattern Detection in Complex Networks: Correlation Profile of the Internet
- Cycles and clustering in bipartite networks