A guide to choosing and implementing reference models for social network analysis

Abstract

Analysing social networks is challenging. Key features of relational data require the use of non-standard statistical methods such as developing system-specific null, or reference, models that randomize one or more components of the observed data. Here we review a variety of randomization procedures that generate reference models for social network analysis. Reference models provide an expectation for hypothesis testing when analysing network data. We outline the key stages in producing an effective reference model and detail four approaches for generating reference distributions: permutation, resampling, sampling from a distribution, and generative models. We highlight when each type of approach would be appropriate and note potential pitfalls for researchers to avoid. Throughout, we illustrate our points with examples from a simulated social system. Our aim is to provide social network researchers with a deeper understanding of analytical approaches to enhance their confidence when tailoring reference models to specific research questions.

Modularity and connectivity of nest structure scale with colony size

“…To determine if observed nests had more branching than expected based on their size, i.e., the number of chambers, or nodes, in the network, we compared the mean distance of networks from observed nests to mean distance of reference models of networks with known branching properties. We evaluated how mean distance relates to nest size under different assumptions about how new nodes are added to a network (i.e., generative models (Hobson et al 2021)). We used three generative reference models that represent the upper and lower bounds on connectivity for how nest networks might increase in size (Buhl et al 2004b; Bebber et al 2007; Tero et al 2010; Latty et al 2011): (1) chain networks (Figure 1A), in which new nodes are added to the last node in a chain – i.e., no branching; (2) triangulated networks (Figure 1C), in which new nodes are connected to at least two other nodes such that they form a triangle while avoiding edge overlap.…”

“…We repeated this process 1000 times for each network size for both triangulated networks and MSTs, because they were probabilistic generative processes, but not for the chain network generation because each size has only one solution. For each generated network, we calculated the mean distance to create reference distributions for comparison with the observed data (Hobson et al 2021; Figure 3B). See R code in the supplementary materials.…”

Knowledge Transfer in a Two-Mode Network Between Higher Education Teachers and Their Innovative Teaching Projects

“…We want to point out that this method of generating randomized networks is a potential limitation of our study. Scholars have already discussed the pitfalls of different procedures for creating randomized networks (e.g., the fit between the randomization procedure and the research question; see Hobson et al, 2021). Another different method of reshuffling data from the one used in this study is the weightreshuffling procedure (Opsahl, 2013;Opsahl et al, 2008).…”

Behavioural variation among workers promotes feed-forward loops in a simulated insect colony

“…Central to these efforts is quantifying the extent to which feed-forward loops and other network motifs are present within colony interaction networks. A common approach is to compare empirical networks with Erdős-Rényi random networks matched for size and density, yet these null models often lack biological and physical relevance [ 58 , 59 ]. For example, random graphs typically assume that all individuals are equally likely to interact, thus ignoring spatial and temporal constraints on interactions (e.g.…”