Background: Graph theory provides a strong mathematical framework for modeling interconnected systems, but its use in different areas, like social networks, transportation networks, and communication networks, is still not fully understood.
Objective: This study seeks to analyze the structural and functional similarities and differences in graph-theoretic models across three domains: social influence propagation, transport routing optimization, and digital communication flow.
Methods: A cross-domain analytical methodology is utilized to evaluate essential graph metrics, encompassing centrality, clustering coefficients, shortest-path algorithms, and network resilience, within domain-specific implementations.
Results: The analysis shows that all three areas have the same basic math principles, but their structures are very different:
•    Social networks show scale-free and small-world properties that are caused by preferential attachment.
•    Transport networks are shaped by space limitations, which leads to planar or almost-planar topologies.
•    Communication networks through hierarchical layering, stress the importance of finding a balance between redundancy and efficiency.
Models also show that they can be used in different fields. For example, epidemic diffusion models can be used to study how information spreads, and shortest-path algorithms like Dijkstra's can be used to route packets.
Conclusion: Graph-theoretic models are very useful across many fields, but there are still some big holes in dynamic graph modeling, real-time scalability, and resilience transferability. Filling in these gaps can make system design, infrastructure planning, and network governance better in all areas.