- GraphTheory, Social Network Analysis, Structural Analysis, Degree Distribution, Connectivity, Directed and Undirected Graphs, Bridges and Cut-Vertices, Eulerian Graphs, Information Flow, Network Stability.
Abstract
The rapid growth of online social networking platforms such as Facebook, Twitter, and WhatsApp has created complex interaction structures that cannot be fully understood using traditional statistical methods alone. This study aims to model and interpret the structural properties of social networks using graph theory as a mathematical framework. In this representation, users are modeled as vertices and interactions such as friendships, follows, and message exchanges are represented as edges. The methodology involves constructing directed and undirected graphs from real-world inspired data and analyzing them using graph-theoretic concepts such as degree distribution, connectivity, paths, cycles, bridges, cut-vertices, bipartite graphs, and Eulerian properties. Important theorems including Eu- ler’s theorem and connectivity principles are applied to identify influential users and com- munication bottlenecks. The results show that the platforms exhibit struc- tures: WhatsApp networks are highly clustered and nearly connected. The study demonstrates that graph theory provides an ef- fective tool for understanding information flow, network stability, and influence patterns in social networks.