Visualization of large networks with min-cut plots, A-plots and R-MAT

Abstract

What does a “normal” computer (or social) network look like? How can we spot “abnormal” sub-networks in the Internet, or web graph? The answer to such questions is vital for outlier detection (terrorist networks, or illegal money-laundering rings), forecasting, and simulations (“how will a computer virus spread?”). The heart of the problem is finding the properties of real graphs that seem to persist over multiple disciplines. We list such patterns and “laws”, including the “min-cut plots” discovered by us. This is the first part of our NetMine package: given any large graph, it provides visual feedback about these patterns; any significant deviations from the expected patterns can thus be immediately flagged by the user as abnormalities in the graph. The second part of NetMine is the A-plots tool for visualizing the adjacency matrix of the graph in innovative new ways, again to find outliers. Third, NetMine contains the R-MAT (Recursive MATrix) graph generator, which can successfully model many of the patterns found in real-world graphs and quickly generate realistic graphs, capturing the essence of each graph in only a few parameters. We present results on multiple, large real graphs, where we show the effectiveness of our approach.