Discussion of “Co-citation and Co-authorship Networks of Statisticians”

We thank the authors for their new contribution to a high quality dataset and interesting findings from the modeling and analysis of the co-citation and co-authorship networks of statisticians. Leveraging this dataset, there are lots of additional questions that might be answered, and analyses done. Network motif analysis is one such, with roots in the triad census of traditional social network analysis (Wasserman and Faust 1994, chap. 14.2.1) and first introduced in its modern form by Milo et al. (2002) in systems biology. It has since been applied to various scientific domains, for example, social science, neuroscience, to study network structures and the underlying complex systems (see Stone, Simberloff, and Artzy-Randrup (2019) for a survey article). While the notion of network motif was originally defined for static networks as small subgraph patterns occurring frequently in a given network, several ways have been proposed to extend it to dynamic networks consisting of a set of vertices and a collection of timestamped edges. One widely used one is from Paranjape, Benson, and Leskovec (2017), where temporal motifs are defined as an ordered sequence of timestamped edges among a subset of nodes conforming to a specified pattern as well as a specified duration of time δ in which the edges must occur. In contrast to their static counterparts, such temporal motifs take into account not only subgraph isomorphism but also edge ordering and duration, which can be regarded as the simple building blocks for temporal structures of dynamic networks. There are a few works in the literature on motif analysis for journal citation networks (Wu, Han, and Li 2008; Zeng and Rong 2021) and author collaboration networks (Chakraborty, Ganguly, and Mukherjee 2015), but none of them seem to be from the perspective of temporal motifs. In this discussion, we construct temporal citation networks among statisticians using the publication data provided in the article, and focus on analyzing the frequency and distribution of temporal motifs in such dynamic networks. This analysis provides initial insights into the temporal patterns of citing behaviors among authors of various statistics journals from 1975 to 2015.