Beyond Binary Ties: Modeling the Evolution of Relational States

R. Juozaitienė

Vytautas Magnus university

Researchers across diverse domains increasingly consider various phenomena from a dynamic network perspective, viewing systems as composed of nodes connected by ties that evolve over time. Most existing modelling approaches, however, rely on binary representations in which relationships are either present or absent. Such representations overlook the heterogeneity and varying intensities that characterize many real-world ties. In practice, relationships often unfold through multiple substantively meaningful states, such as acquaintanceship, friendship, or collaboration, that reflect relatively stable relational conditions rather than isolated interactions. Reducing these states to a binary structure loses important information about how ties emerge, intensify, and dissolve.

To address this limitation, we introduce a continuous-time framework for modelling dynamic networks in which each dyad occupies one of several distinct relational states and evolves through transitions between them. Building on relational event models, we treat state transitions as probabilistic events and model the waiting times between them using hazard-based approaches. Transition rates are allowed to depend on endogenous network structures—such as reciprocity and triadic closure—as well as exogenous covariates. Extending relational event models to multi-state settings requires novel definitions of endogenous network effects and estimation strategies capable of capturing the added structural complexity. The proposed framework provides a flexible approach for analyzing the evolution of relational states while preserving the substantive richness of network dynamics.

Keywords: multi-state ties, relational states, dynamic networks