Value can depend on who else is there.
A communication tool can become more useful when more of the people you want to reach use it. Each additional member introduces new possible pairs. With n members there are n(n − 1)/2 distinct undirected pairs.
The experiment separates that possibility from actual connections. Each pair connects independently with the probability you choose. Hollow circles have no direct connections in the sampled network.
Inside this model
This is a small undirected random graph with no self-links or duplicate edges. At 0% connection chance there are no edges. At 100%, every possible pair is connected.
Connections are only an illustrative proxy for opportunity. The simulation does not assign economic value, and it does not assume that indirect connections are as useful as direct ones.
Why it matters
Adoption and usefulness can reinforce one another when people gain from sharing a network. But a member count alone leaves out who can connect and why they would want to.
A useful lens. Not a universal law.
- Real relationships are not independent or equally likely. Clusters, geography, compatibility, and personal preferences matter.
- Congestion, spam, moderation costs, and poor-quality interactions can offset benefits. More possible pairs do not guarantee more value.
Further reading
Easley and Kleinberg distinguish the direct benefits of network participation from copying others for information.
Networks, Crowds, and Markets — Network Effects ↗