Plotting decay in clustering?

Question

I've got a method that produces clusters of elements and singletons. The singletons usually comprise about half of the initial element set, and there usually is a single biggest cluster of a several million elements, followed by a second cluster of a few hundred thousand elements, then the rest of the clusters with thousands to hundreds of elements.

I would like to plot this in a way that lets me compare different sets that have initial element sizes. For example, set 1 can have 30 million elements, but set 2 can range from 5 million elements to 50 million elements. How can I plot these characteristics of decay of clustering in a way that is normalized for comparison of multiple sets of different element size?

Answer 1

I've used plots of the following type. X-axis denotes cluster size on a logarithmic scale, so you'd have 1, 10, 100, ... 100,000,000 at regularly spaced points. Y-axis denotes 'Cumulative fraction of the number of nodes contained in clusters of size x or less' -- so y ranges from 0.0 to 1.0. I think if you simply rescale the X-axis to a fixed width you should get comparable plots. Such plots are quite informative for clustering granularity. (Examples can be found at pages 292 and 293 of 'Bacterial Molecular Networks', edited by van Helden et al.).