This diagram is taken from an old hand-coded page full of them, some of which will appear on this site in other posts. That page, written in HTML, dates from 2004.
It illustrates how a poorly linked social network can be improved using an optimization algorithm. The width of the lines represent the level of compatibility and effectiveness of communication between the individuals. The Before diagram shows a network with missing links which isolate some groups of people from the rest. None of those links are as good as those in the second diagram, obtained by just changing who is connected to whom.