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**Fitting the linear preferential attachment model.**
*(English)*
Zbl 1387.62074

The evolution of a network can be described by the preferential attachment mechanism in which edges and nodes are added to a network with certain probabilities. In general, the in- and out- degree distributions follow a power law. The authors discuss methods for fitting a 5-parameter linear preferential model to network data when full history of the network formation is known as well as when only a single-time snapshot of the network is available. In the former case, MLEs of the parameters are derived and shown to be strongly consistent and asymptotically normal. In the second case, an estimator based on method of moments combined with an approximation to likelihood is proposed which is also strongly consistent and behaves as well as the MLE. Both estimation procedures are illustrated by simulations. The authors give a lucid introduction and details of the mathematical results and acknowledge an efficient algorithm by Joyjit Roy “designed to capitalize on the linear growth structure”.

Reviewer: T. J. Rao (Visakhapatnam)