Electricity: about 210,000 electrical transmission substations provide the world with power for their gadgets, climate control devices, and now cars. source
GIMPS: about 130,000 number fans run the Great Internet Mersenne Prime Search program to help find the next big prime number. source
The internet: about 66,000 ISPs connect houses, businesses, and smartphones to the information superhighway. source
Bitcoin: about 66,000 bitcoiners run the nodes that keep the world’s best money running nonstop since 2009. source
Pro radio: about 44,000 corporate radio stations keep the world entertained, informed, and misinformed. source
Television: about 36,000 tv stations do the same stuff radio stations do but more immersively/addictively/expensively. source
Train stations: about 36,000 train stations connect the cities of Europe to one another as well as servicing inner-city stops. source I found no worldwide estimate, but my wild speculation is this: the real total would place the railway network just above electricity. If each populated continent has about as many stops as Europe does, then 36k * 6 = 216k train stations.
Ham radio: about 19,000 amateur radio operators in the USA run "repeaters" to transmit text and audio across the ham radio network. source I found no worldwide estimate, but my wild speculation is this: the real total would place ham radio between bitcoin and GIMPS. If each populated continent has about as many ham relays as the USA does, then 20k * 6 = 120k repeaters.
Lightning: about 12,000 people run the public infrastructure of the open source world’s most successful and popular second layer payment system. source
PrimeGrid: about 11,000 math-minded men and women run the nodes of the biggest prime-finding computer network not named GIMPS. source
Highways: about 10,000 cities serve as nodes of the world’s various interstate highway systems, and as of 2015, analysts guess that about 48% of the world’s human inhabitants live in them. source
Air traffic: about 9,000 commercially operated airports keep people connected to all of the world’s largest cities and an incredible number of its smaller ones too. source
Tor: about 8,000 anons keep the onion network private by running the system’s snoop-stopping software. source
Ethereum: about 5,000 woefully bored people run the infrastructure to keep this particular rugathon from finally dying. source
I don't know any other network with more than 5,000 nodes, excluding natural networks like galaxies/mycelia/brains, and digital simulations of large networks e.g. neural nets.
I also considered putting in a section for city bus networks; some cities have records about the number of bus stations in their network, which seems like a decent starting point; but I didn’t want to list every city bus network, so I figured I’d give an average.
Which meant I needed an “average” city. With my estimate of 10k cities (see the section on Air Traffic) and that about half of the world population live in them (see the same section), I figured an “average” city has about 400,000 people in it (8 billion / 2 = 400,000). I looked up cities with that amount and found Tulsa, Oklahoma as a decent example of an “average” city.
But its bus system is visible here and by looking at it, I figure it has about one or two hundred bus stops. Which isn’t enough to go on my list. So I figure if an “average” city doesn’t have a big enough bus system to go on my list, I won’t put any of them on my list. Also, if you combine inner-city buses with inter-city buses to get a more complete idea of the worldwide bus network...well, you just get the highway system, which I already covered.