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.