A Verified Relationship Graph Framework for Population Estimation in Data-Scarce Environments

Abstract Traditional census methodologies encounter critical and often insurmountable failures in sub-Saharan Africa owing to inaccessible terrain, prolonged conflict, informal settlement structures, systemic political interference, and severe resource constraints (United Nations Population Fund [UNFPA], 2023; Jerven, 2013). Nigeria's 2006 census is internationally recognised as the most recent nationally accepted demographic enumeration. The 2006 Census has left an estimated population exceeding 220 million people without verified demographic data for nearly two decades (National Population Commission [NPC], 2007; Woldemariam, 2019). This paper proposes the Verified Relationship Graph (VRG) framework, a novel approach wherein individual persons are modelled as nodes in a directed graph and familial relationships as independently verified edges, enabling robust population estimation through relationship-expansion traversal. Unlike self-reported surveys, which are prone to systematic incentive distortions (Setel et al., 2007), VRG requires each claimed relationship to be corroborated by a common node possessing mutual ties to both parties, substantially reducing fraudulent registration while preserving coverage. This paper present the theoretical foundations of the framework, formulate a graph neural network (GNN) architecture for probabilistic population inference, and demonstrate a simulated case study calibrated to Nigeria's known demographic structure. Findings suggest that VRG offers a scalable, fraud-resistant complement to conventional census methods in environments where enumeration is structurally compromised.