Anomalous scaling in redirection networks
This work addresses scaling properties in network growth models, which is incremental as it builds on existing isotropic redirection frameworks to provide analytical insights.
The paper tackled the problem of anomalous scaling in networks that grow by isotropic redirection, where leaf proliferation leads to sublinear scaling of nonleaves as N^μ and an algebraic degree distribution with exponent 1+μ. The result was the introduction of a new model with redirection to leaves, which avoids non-locality and allows analytical extraction of the exponent μ.
In networks that grow by isotropic redirection (IR), a new node selects an initial target node uniformly at random and attaches to a randomly chosen neighbor of the target. The emerging networks exhibit leaf proliferation, in which the number of nonleaves scales sublinearly as $N^μ$ and the degree distribution has an algebraic tail with exponent $1+μ$. To understand these mysterious properties, we introduce a class of models with redirection to leaves whenever possible. The resulting networks exhibit qualitatively similar phenomenology to IR networks, but avoid the inherent non-locality of the IR growth rule. These networks admit an analytical description of the leaf degree distribution, from which we extract the exponent $μ$.