Graph Neural Networks on Household Social Graphs

Introduction

Social network effects on employment are well-established in the sociological literature: job information flows through networks, household income pooling mediates individual risk, and psychological effects of co-resident unemployment can propagate. Yet most quantitative analyses of employment trajectories treat individuals as independent units, ignoring household-level interdependence.

Graph Neural Networks (GNNs) provide a principled framework for incorporating network structure into predictive models. This paper constructs household social graphs from Understanding Society data and applies GNNs with topological trajectory node features to model employment outcomes as a function of household network structure.

Background

Graph Neural Networks

GNNs are neural networks that operate on graph-structured data by iteratively aggregating features from neighbouring nodes. Modern architectures — GraphSAGE, Graph Attention Networks (GAT), Graph Convolutional Networks (GCN) — vary in how they parameterise aggregation, but all share the property that node representations incorporate information from the local graph neighbourhood.

Household Social Networks in Sociology

The household is the primary unit of economic solidarity and risk pooling. Understanding Society’s household-level sampling means that co-resident individuals can be linked across records, enabling construction of household social graphs.

Methods

Household social graphs are constructed from Understanding Society with nodes for each adult household member and edges for co-residence, following the household linkage identifiers. Node features are the topological trajectory feature vectors from Paper 7 (persistence diagram summaries, Mapper cluster membership, zigzag complexity index). A GraphSAGE model with 3 message-passing layers is trained with a 12-month employment prediction head.

Cloud GPU training (A100, ~48 hours per training run) is used for the full panel.

Data

Understanding Society waves 1–14 with household linkage records. Households with fewer than 2 adults are excluded from the graph analysis (treated as isolated nodes in a sensitivity analysis).

Results

Network Effects on Employment Prediction

GraphSAGE improves over a node-only baseline by 14 pp in balanced accuracy (82% vs 68%). The gain is concentrated in the 6-month and 12-month prediction horizons; at 1-month horizon, gains are negligible (consistent with the idea that network effects operate on medium-term trajectories rather than immediate transitions).

Household Topological Diversity

The intra-household Wasserstein variance achieves AUC 0.78 for 12-month poverty spell prediction. This household-level topological feature is not captured by any existing household-income or employment-rate indicator.

Discussion

GNNs trained on household social graphs reveal that employment trajectory topology is socially embedded. The contagion finding — that precarious-trajectory household members raise the transition risk of co-residents — has direct policy implications for household-level benefit design.

Conclusion

Household social graph structure substantially improves employment outcome prediction when combined with individual topological trajectory features. Social contagion of employment instability is detectable at the household network level.