Percolation theory illuminates the behavior of many kinds of networks

Kelsey Houston-Edwards in Scientific American:

When you hit “send” on a text message, it is easy to imagine that the note will travel directly from your phone to your friend’s. In fact, it typically goes on a long journey through a cellular network or the Internet, both of which rely on centralized infrastructure that can be damaged by natural disasters or shut down by repressive governments. For fear of state surveillance or interference, tech-savvy protesters in Hong Kong avoided the Internet by using software such as FireChat and Bridgefy to send messages directly between nearby phones.

These apps let a missive hop silently from one phone to the next, eventually connecting the sender to the receiver—the only users capable of viewing the message. The collections of linked phones, known as mesh networks or mobile ad hoc networks, enable a flexible and decentralized mode of communication. But for any two phones to communicate, they need to be linked via a chain of other phones. How many people scattered throughout Hong Kong need to be connected via the same mesh network before we can be confident that crosstown communication is possible?

More here.