Seed circulation among farmers, which is embedded in composite social networks, is a key process in the dynamics of seed systems that shape crop diversity. We analyzed the daily circulation of biological objects, i.e., cultivated plants (31 species, 284 landraces), within a community of first-generation migrants (16 households, 30 persons) living on the island of Vanua Lava in the South Pacific archipelago nation of Vanuatu. By combining participant observation, ethnobiological inventories, and social network analysis, we investigated how farmer social status and plant biocultural value affect plant circulation. Plant biocultural value was estimated by referring to their local classification according to uses, cultivation practices, growing environments, and biological properties. An aggregate plant circulation network (577 events) and three subnetworks (i.e., for starchy, side dish, or snack food categories) sharing the same 30 nodes were analyzed using exponential random graph models. Evidence that farmer social status influences the patterns of plant circulation was found through the distribution of structural parameters of the network, including: dyadic reciprocity; in-degree, out-degree, and their correlation; triadic cycling; and transitivity. At the scale of the aggregate network, direct or indirect reciprocity was not observed. Instead, a high out-degree (i.e., being a more frequent giver) and a negative correlation between in-degree and out-degree both confer prestige and reinforce hierarchy. These results suggest that some of the social dynamics of the Melanesian-type Big Man political system may persist, even though the system itself no longer exists in traditional form. Moreover, based on our comparative analysis of the three subnetworks, farmer social status appears to influence greatly the circulation of plants with high biocultural value while having little influence on plants with low biocultural value. Farmer social status and plant biocultural value (following their local classification) are important factors for understanding the social rules shaping seed circulation.