Why one more user can add many connections
A network’s usefulness can grow faster than its user count because each new participant can create a link with people already there. If a service has 100 users, adding one more creates 100 new possible user-to-user pairs—not just one new participant. Those links might support messages, calls, trades, or other interactions, depending on what the network is for.
This is the intuition behind network effects: a product can become more valuable to an individual as more people use it, because there are more potential people to reach. The effect is especially clear in communication networks. A phone is useful partly because other people have phones; a messaging app becomes more useful when the people you want to contact are on it too.
Why the count accelerates
With n participants, the number of distinct pairs is n × (n − 1) ÷ 2. Each pair is counted once, so the formula avoids treating A-to-B and B-to-A as separate connections. The total therefore rises roughly with the square of the population: doubling the users can produce about four times as many possible pairs.
But a possible link is not necessarily a real or useful one. People may never meet, may not want to interact, or may use the service for different purposes. A network can also become harder to navigate as it grows, and the value of an additional user depends on whether that person connects with others in a meaningful way.
That distinction explains why a growing user count can signal greater potential without proving that every user benefits. The striking part is the combinatorics: one new person can open a door to every existing member, even though no one is required to walk through it.
