Empirical articles vary considerably in how they measure child and adolescent friendship networks. This meta-analysis examines four methodological moderators of children’s and adolescents’ average outdegree centrality in friendship networks: boundary specification, operational definition of friendship, unlimited vs. fixed choice design, and roster vs. free recall design. Specifically, multi-level random effects models were conducted using 261 average outdegree centrality estimates from 71 English-language peer-reviewed articles and 55 unique datasets. There were no significant differences in average outdegree centrality for child and adolescent friendship networks bounded at the classroom, grade, and school-levels. Using a name generator focused on best/close friends yielded significantly lower average outdegree centrality estimates than using a name generator focused on friends. Fixed choice designs with under 10 nominations were associated with significantly lower estimates of average outdegree centrality while fixed choice designs with 10 or more nominations were associated with significantly higher estimates of average outdegree centrality than unlimited choice designs. Free recall designs were associated with significantly lower estimates of average outdegree centrality than roster designs. Results are discussed within the context of their implications for the future measurement of child and adolescent friendship networks.

We introduce a class of non-uniform random recursive trees grown with an attachment preference for young age. Via the Chen–Stein method of Poisson approximation, we find that the outdegree of a node is characterized in the limit by ‘perturbed’ Poisson laws, and the perturbation diminishes as the node index increases. As the perturbation is attenuated, a pure Poisson limit ultimately emerges in later phases. Moreover, we derive asymptotics for the proportion of leaves and show that the limiting fraction is less than one half. Finally, we study the insertion depth in a random tree in this class. For the insertion depth, we find the exact probability distribution, involving Stirling numbers, and consequently we find the exact and asymptotic mean and variance. Under appropriate normalization, we derive a concentration law and a limiting normal distribution. Some of these results contrast with their counterparts in the uniform attachment model, and some are similar.

We consider growing random recursive trees in random environments, in which at each step a new vertex is attached (by an edge of random length) to an existing tree vertex according to a probability distribution that assigns the tree vertices masses proportional to their random weights. The main aim of the paper is to study the asymptotic behaviour of the distance from the newly inserted vertex to the tree's root and that of the mean numbers of outgoing vertices as the number of steps tends to ∞. Most of the results are obtained under the assumption that the random weights have a product form with independent, identically distributed factors.