  All real networks are different, but many have some structural properties in
common. There seems to be no consensus on what the most common properties are,
but scale-free degree distributions, strong clustering, and community structure
are frequently mentioned without question. Surprisingly, there exists no simple
generative mechanism explaining all the three properties at once in growing
networks. Here we show how latent network geometry coupled with preferential
attachment of nodes to this geometry fills this gap. We call this mechanism
geometric preferential attachment (GPA), and validate it against the Internet.
GPA gives rise to soft communities that provide a different perspective on the
community structure in networks. The connections between GPA and cosmological
models, including inflation, are also discussed.
