The topology of a family tree graph and its members’ satisfaction with one another: a machine learning approach

Background Family members’ satisfaction with one another is an important component of family well-being, yet most quantitative studies examine specific dyadic or household-level variables rather than the overall topology of the family tree. Methods We present an exploratory machine-learning framework for studying whether family-tree topology contains predictive information about reported family satisfaction. In the proposed approach, each family is represented as a topology-only graph whose nodes correspond to family members and whose edges encode family relationships. A Variational Graph AutoEncoder (VGAE) is used to obtain latent graph representations, which are then used in supervised regression models to predict Extended Family Satisfaction (EFS) and Nuclear Family Satisfaction (NFS). The approach is evaluated on a self-selected online convenience sample of N = 486 families recruited through social-media platforms, using a family-level train/test protocol. Results The proposed topology-based representation showed predictive performance for reported family satisfaction and was compared with regression models based on established aggregate family variables and additional graph-based baselines. These results suggest that family-tree topology may contain information relevant to reported satisfaction, although the evidence remains predictive and exploratory. Conclusion The findings provide preliminary evidence that graph-based representations of family structure can support the study of family satisfaction. However, the results should not be interpreted as causal or population-level conclusions, given the study’s sampling limitations, low response rate, and absence of sociodemographic control variables.