Introduction to Network Science: From Graph Theory to Complex Relational Systems

Network science is often introduced as the study of nodes and edges, but such a definition is too spare to capture the kinds of systems the field now investigates.Real networks are heterogeneous, dynamic, layered, spatially embedded, semantically structured, and often shaped by feedback between local interaction and system-level organization.This paper offers a broader and more conceptually precise introduction to network science by distinguishing it clearly from graph theory, clarifying the different intellectual priorities of each, and showing why relational modelling has become strategically important across science, engineering, public policy, and digital society.It also situates recent work in transport resilience, walkability, dynamic knowledge graphs, narrative and media analysis, and emerging technological themes within a wider network-science agenda.The aim is not to dilute mathematical rigor, but to show that rigor connected to empirical systems, explanatory depth, and intervention.