Structure of growing networks with no preferential attachment

This notebook illustrates the asymptotic behavior of the degree distribution for highly clustered networks.  In particular, it tries to explain the formation of structural properties under the two following conditions:

  • The formation of links cannot be described according to the principle of preferential attachment; and
  • The in-degree distribution fits a power law for nodes with a high degree and an exponential form otherwise (i.e., an extended power).

Extended power laws are – in some contexts – a better fit than single or double power laws, e.g., to describe the degree distribution of online social networks and patent citation networks. Our paper characterizes the relation between the scaling exponent and the probability of forming triads. The transition from exponential to power law distributions depends on both the scaling exponent and the number of links that newly added nodes establish. Note that the underlying mechanism accounts for strong neighborhood clustering based on a random triad formation process. Average clustering properties remain constant as the size of the network grows. To download the notebook click here.