Andrej Srakar’s contribution to the Discussion of ‘Root and community inference on the latent growth process of a network’ by Crane and Xu

原文摘要

Paper presented by Harry Crane and Min Xu develops a rather novel area of network archaeology, which builds on findings of network science, probability theory and (in Crane and Xu's article) Bayesian statistics. My comments are directed to possible extensions for future work in this promising area of research. Firstly, in terms of network stochastic processes (authors use a combination of preferential attachment and Erdős–Rényi models) paper does little to explain comparisons with possible alternatives. Briend et al. (2023) discuss network archaeology in a random recursive dags and Cooper–Frieze random networks contexts, and Brandenberger et al. (2022) in the more general context of Bienaymé–Galton–Watson trees. I wonder if topology of the studied network could be incorporated in more detail, for example in today often studied weak-topology context (for example in Gromov-weak or just general Skorokhod topologies). This would need different metric spaces and distance metrics where results for different types of random graphs and trees are wide and could be useful for the development of the area as well for its extensions of studying the asymptotic behaviour and estimation. Combination with graphon perspectives which authors mention in the introduction would also be interesting to explore, as well as addressing the possibilities noted by Brandenberger et al. of extensions to k-ary, Cayley, Motzkin and planted plane trees as well as branching stochastic processes in general. Secondly, it seems to go unexplained why the authors are using Bayesian approach. The Bayesian component in the article seems underexplored and many possibilities could be useful for future developments of the used priors as well as Gibbs sampling procedure (authors themselves mention mixing properties of the sampler). Extensions of the Bayesian part could go in the direction of intractable likelihood perspectives, computational improvements (say, using integrated nested Laplace approximation) or in the selection of priors (parametric, semiparametric, or nonparametric perspectives or even to empirical Bayes possibilities). Study of the Bayesian asymptotic properties here would be very interesting. Finally, I miss more explicit and broad connection to the study of temporal networks and network in general. Not only root vertex and communities could be discovered, but connection to cliques, islands, and homophily as well as many possible types of networks based on characteristics of their ties, such as affiliation, weighted, multi-relational, or multi-layer networks. Possibilities for future research in this area of network science could loom large. The following contributions were received in writing after the meeting:

摘要来源：OpenAlex