You don't actually need to live near people to form a tight-knit circle; a couple of super-influential people are enough to pull everyone into the same orbit.
arXiv · March 16, 2026 · 2603.13159
Why it matters
It has long been assumed that if your friends all know each other, it's because you share a common 'geometry' like a neighborhood or a hobby. This paper proves that these tight-knit clusters can form with no underlying space at all, simply as a result of how 'fitness' or popularity is distributed across the network.
From the abstract
The coexistence of sparsity and clustering (non-vanishing average fraction of triangles per node) is one of the few structural features that, irrespective of finer details, are ubiquitously observed across large real-world networks. This fact calls for generic models producing sparse clustered graphs. Earlier results suggested that sparse random graphs with independent edges fail to reproduce clustering, unless edge probabilities are assumed to depend on underlying metric distances that, thanks