A Dual-Graph Framework for Modelling and Analysis of Movements and Activities

Graph-based representations provide a useful systems-level framework for modelling interactions among structure, dynamics, and behaviour.This paper proposes a dual-graph framework for modelling indoor movements and activities.The first layer is a location graph that represents feasible movement through the spatial connectivity of an indoor environment.The second layer is a mixed causal/contextual activity graph that combines directed activity dependencies with undirected contextual associations.The two layers are coupled through an activityto-location mapping, yielding a probability-preserving dynamical model in which spatial occupancy is jointly influenced by graph-constrained movement and activity-driven spatial expectations.Two features distinguish the proposed framework from conventional dual-graph models.First, the activity layer is explicitly constructed as a mixed directed/undirected network and second, a cross layer coupled mismatch residual framework is proposed to detect inconsistencies between semantic activity evolution and observed movement.The paper also establishes the probabilistic properties of the movement operator, discusses manual and data-driven construction of the interlayer mapping and introduces an optional reverse-coupling extension.Simulations in a six-location living environment examine the effects of the activity-mixture parameter, the mapping matrix, and the coupling gain.The results support the framework as an interpretable basis for indoor behaviour modelling and also highlight some of its limitations for future studies.