Network-cycle motif participation is associated with individual and collective wealth in Honduran villages

Geodesic cycles, or loops of nodes connected in a sequence within a network, are an important if under-studied network motif, and their prominence or deficiency is associated with both beneficial and detrimental properties in diverse kinds of networks. Here, we examine cycles formed by people's reports of informal borrowing/lending and friendship ties among 22,551 rural Hondurans (in 174 isolated villages), and we explore their association with personal and community wealth across two time points. We find that cycles of different lengths (i.e., 3 or 4 ties in a loop) constitute an over-represented motif, and their quantity is strongly associated with individual wealth, i.e., richer individuals are involved in more cycles. Furthermore, we introduce a new metric of cycle composition, defined as the average of some measure (e.g., wealth) of a node's alters in its cycles, and find that this metric outperforms cycle quantity as an indicator of both current and future wealth. A longitudinal analysis also reflects a higher participation rate in future cycles among wealthier individuals. When benchmarking cycles with eigenvector centrality, we find that cycle participation offers distinctive insights. Finally, cycle composition is a strong indicator of overall village wealth. In sum, the potential for the flow of money in a village through structural social network cycles may relate to both individual-level and village-level wealth.