Abstract
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.
Highlights
All real networks are different, but many have some structural properties in common
A new node t connects to an existing node s, t if s is both popular enough and similar to t, that is if sbhst is small, where b [ 1⁄20,1 is a parameter that controls the relative contributions of popularity and similarity
Using the Autonomous Systems (AS) Internet topology as example, we have seen that the geometric preferential attachment (GPA) mechanism generates heterogeneous networks that are similar to real networks with respect to key properties, including key aspects of the community size distribution and separation
Summary
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. For social networks, where there is a strong relationship between a high concentration of triangles and the existence of community structure[28], triadic closure[29] has been proposed as a plausible mechanism for generating communities[30]. It was shown by means of a simple agent-based acquaintance model that a large-scale community structure can emerge from the underlying social dynamics[31]. There exist other contributions in this direction, where proposed mechanisms and generative models are tailored for social networks[32,33,34,35]
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