Sampling from naturally truncated power laws: The matchmaking paradox
Abstract
Consider a network of M >> 1 nodes connected by N >> 1 links, in which the distribution of the number of links per node follows a power law with exponent 0<α <1. The power law is naturally truncated due to the fact that N is finite. A subset of m << M nodes is sampled arbitrarily, yielding the sample mean η : The average number of links per node, within the sampled subset. We explore the statistics of the sample mean η and show that its fluctuations around the population mean =N/M are extremely broad and strongly skewed -- yielding typical values which are systematically and significantly smaller than the population mean . Applying these results to the case of bipartite networks, we show that the sample means of the two parts of these networks generally differ -- the fact we call "matchmaking paradox" in the title.