Network Analysis Using Graph Indices

Abstract

In the digital age, social networking platforms like Twitter, LinkedIn, and Facebook have significantly influenced how individuals interact and form communities. These platforms, along with transportation networks, play crucial roles in shaping social dynamics and fa- cilitating physical mobility. This thesis employs graph theory to analyze these networks, focusing on the complexities of their interactions using Graph Indices, a mathematical framework that enhances the precision of network analysis. Graph theory provides a robust foundation for understanding the structure and flow of information within networks. This study specifically utilizes concepts such as betweenness centrality and the beta index to an- alyze network properties. Betweenness centrality identifies key influencers by measuring how often a node lies on paths between other nodes, while the beta index assesses network complexity by calculating the ratio of edges to vertices. The research encompasses a de- tailed examination of subgraphs, which reveal clusters or communities within the network, providing insights into user behavior and network dynamics. This analysis is applied to various social networks and transportation systems, demonstrating how graph indices can be used to optimize and enhance network structures. By integrating Graph Indices into graph theory, this study offers a more versatile framework for capturing social interactions’ complexities. The findings underscore the importance of mathematical tools in developing strategies for managing and leveraging social networks, leading to improved efficiency and robustness of network systems. This research not only advances theoretical understand- ing but also provides practical solutions for network analysis, paving the way for future applications in the field.