Fig. 4: Multilevel social network structures.

A graphical illustration of the key locally specified multilevel network structures in our network model, with inter-household ties existing within an isigodi and across izigodi. A darker colour indicates the household h (circle, in blue) or the region v (square, in red) has experienced an outcome change over time, whereas a lighter colour indicates others. We model three regional-based social connectivity effects for the household-level outcome: for example, the likelihood of a household experiencing an asset change (\(\left|\Delta {w}_{h}\right| > 0\)) may be dependent on whether they have shared a tie to a household in the same isigodi (Fig. 4a), different isigodi (Fig. 4b), or outside of the DSA (external ties, Fig. 4c). External ties refer to households having non-residents at baseline (i.e., circular migrants). We model two regional-based network interaction effects, in which the likelihood of a household experiencing an asset change is dependent upon whether asset changes had also occurred among their network partners residing in the same isigodi (Fig. 4d) and/or different izigodi (Fig. 4e). For the regional-level outcome (\(\Delta {{Inq}}_{v}\ge .02\)), we examine whether rising inequality observed at the regional level is associated with their level of inter-household social connectedness (Fig. 4f), or by having many cross-region inter-household ties (Fig. 4g). Figure 4h indicates the likelihood of two interconnected regions (linked by inter-household ties) simultaneously experiencing a rise in their inequality scores over time. Finally, we introduce a cross-level interaction effect to examine whether the regional-level inequality outcome may be driven by network interaction processes within a shared geography – an indication of the theorised emergence of network-driven inequality (Fig. 4i).