Figure 1. Growth of the largest component in large networks at the threshold: This figure demonstrates the rapid growth of the giant component in large networks near the threshold level of concurrency.

The top row shows histograms of the momentary degree distribution for networks at mean degree 1.68, 1.74, 1.80 and 1.86, corresponding to 56, 60, 64 and 68 percent of sexually active persons having concurrent partners. The bottom row gives a visualization of a typical largest component. We can see that the percentage of the population in the largest component jumps rapidly from 2% to 64% with a very small increase in mean degree (0.2 of a partner, 12% more persons with concurrent partnerships).