It is the crossings between them. Here is the map of one. Every line is a person. Every ring is two people who actually cross: talk, trade, help, argue, show up. Watch what adding one person does to the number of possible crossings.
People add up; crossings multiply. Three people have three crossings, ten have forty-five, thirty have four hundred and thirty-five. Every person you welcome brings a line; the community gets the interchanges.
A crossing needs a place to happen: the bench, the pinboard, the Thursday table, the shared tool shed. Whoever builds the places where lines can cross is building the community, whatever their job title says.
Loneliness, on this map, is a geometric fact: a line running parallel to all the others. The fix is never "more people." It is one new crossing, built close enough to reach.