Graph Analytics for Social Networks

Abstract

- Social networks generate vast amounts of relational data whose value lies not in individual data points but in the structure of connections among them. Graph analytics offers a mathematically grounded toolkit for uncovering this structure, ranging from simple degree counts to sophisticated community-detection and influence-propagation models. This paper presents a self-contained treatment of graph analytics as applied to social networks. We review the foundational graph-theoretic concepts underlying social network analysis, survey the principal families of graph analytics methods, and examine community detection and influence analysis in depth. To ground the discussion empirically, we conduct a case study on Zachary's Karate Club network and a synthetically generated scale-free network, computing centrality measures, detecting communities using the Louvain algorithm, and analysing degree-distribution behavior. The Louvain method partitions the Karate Club network into four communities with a modularity of 0.4266, closely matching the network's known factional split, while the synthetic network exhibits an approximate power-law degree distribution with exponent 1.76, consistent with preferential-attachment growth. We conclude with a discussion of open challenges and directions for future research, including dynamic graph analytics, scalability to billion-edge networks, and privacy-preserving analysis.