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How fast can I infect the world?

I look here at a random selection of 500 individuals from the New Orleans Facebook regional network. For each person I calculate what the size of their neighborhoods of orders \(1, 2, ..., 8\) to see how quickly they could infect the world if they had a hyper-deadly virus.

The short answer is really quickly. After 4 friends, more than 3/4 of them have infected more than half of the population (I know, confusing…).

Here’s a plot of their trajectories:

It’s a bit clearer if we look at boxplots. We can read off for example that after 4 steps (friends of friends of friends of friends) we’re at more than half of the population for 75% of cases.

And of course violin plots are beautiful, so why not show the data that way as well?

The order of increase in neighborhood size

We can examine the factor increase. That is, how many times does the neighborhood increase in size at each order?