A Multilayer Graph-Theoretical Framework for Agrotourism Network Analysis in Shkod\"{e}r County, Albania

Agrotourism offers a pathway for sustainable rural development, yet its potential is often constrained by fragmented stakeholder networks and limited understanding of their structural dynamics. This paper introduces a multilayer graph-theoretical framework to model, analyze, and optimize the agrotourism ecosystem of Shkod\"{e}r County, Albania—a region of rich natural and cultural heritage hindered by infrastructural and digital deficits. We construct a weighted multilayer network and propose three innovations: cross-layer centrality influence, seasonal dynamic modeling, and robustness analysis under node and edge failures. Empirical analysis of 32 agrotourism sites, GIS road networks, and social-media data reveals a core-periphery structure: urban hubs exhibit high centrality, while high-tourism nodes like Theth suffer from physical isolation. Community detection identifies three functional clusters—urban-hub, agri-coastal, and highland-tourism—each requiring tailored interventions. Our optimization model shows that a hybrid investment strategy combining digital inclusion with targeted road improvements yields a \(9.1\%\) increase in network efficiency, outperforming purely infrastructural approaches. This replicable framework offers a data-driven blueprint for transforming fragmented rural economies into resilient, interconnected systems across the Western Balkans.