Expanding Horizons: Graph Theory’s Multifaceted Applications

Abstract

A subfield of mathematics called graph theory studies networks of points interconnected by lines. Researchers may model and examine the structure of a network using graph theory. Mostly topological in nature, graph theory supports both qualitative and quantitative methods. Important scientific findings have been made possible by graph theory, including a better understanding of how electrical distribution systems malfunction and how health problems spread through social networks. Although network analysis typically conjures images of graph theory, complex network theory, and network optimisation, geographers employ a variety of techniques to study networks. This study emphasises the foundational significance of graph theory in modelling and analysing complicated networks by methodically exploring the many applications of graph theory throughout several fields. It starts with a review of the fundamental roles that graph theory plays in mathematical information, computational science, and chemistry. The discussion then moves to cutting-edge applications in the fields of social media, means of transport, and the field of neuroscience, demonstrating graph theory’s versatility. The research emphasises its new application in improving traffic flow projections and assessing cultural environmental amenities employing social media data. The present article validates the crucial role of graph theory in addressing contemporary issues through an extensive overview and methodological study.

Keywords

• graph theory
• applications
• engineering
• mathematics
• computer science