Graph Parameters for Social Network Analysis

Abstract

The exponential growth of complex networks has transformed social network analysis, creating unprecedented challenges for community detection. As networks scale to billions of nodes and connections, traditional approaches struggle to capture the true nature of community structures. This thesis addresses three fundamental limitations in current methodologies: inadequate integration of node importance, limited similarity measures, and inflexible optimisation approaches. Through theoretical development and experimental validation, this research presents three innovative contributions that significantly advance community detection capabilities. The first contribution is the Neighbourhood overlap and Density (NoD) similarity measure, which combines information about shared connections with local structural density. This novel measure overcomes limitations in traditional approaches by considering both how many neighbours two nodes share and how densely those shared neighbours are connected. Experimental validation on real-world benchmark networks—including Zachary’s Karate Club, Dolphins, Football, and Polbooks—shows that NoD increases modularity by up to 0.08 (from 0.38 to 0.46 on Dolphins) while maintaining competitive accuracy with Normalised Mutual Information (NMI) values ranging from 0.71 to 0.90 across the evaluated datasets. Building upon NoD, two complementary algorithmic contributions address distinct community detection scenarios. The Heuristic Community detection algorithm based on Centrality and Similarity measures (HCCS) introduces a deterministic approach that recognises the varying importance of nodes in community formation. By systematically integrating centrality-based leader selection with similarity-driven community formation, HCCS overcomes the limitations of traditional approaches that treat these aspects separately, resulting in more accurate and robust community detection. Experimental evaluation across nine real networks—from small social graphs to large infrastructure and communication networks—using modularity and Normalised Mutual Information confirms its effectiveness, delivering the highest modularity on Karate (0.42), Football (0.60), and Uni_email (0.55) and competitive NMI scores such as 0.89 on Dolphins and 0.90 on Football while preserving reproducible results

The Ant Colony Optimization Based on Centrality and NoD Similarity (ACOCNoD) algorithm extends detection capabilities to overlapping community structures, where nodes can belong to multiple communities simultaneously—a common characteristic in real-world social networks. ACO-CNoD incorporates adaptive mechanisms that automatically adjust to different network characteristics without requiring manual parameter tuning. Comprehensive evaluation on the same benchmark suite, complemented by the overlapping-heavy Pretty Good Privacy (PGP) network, shows that ACO-CNoD achieves the top overlapping modularity (Qov) on five of seven datasets (e.g., 0.72 on Karate and Dolphins, 0.709 on Jazz_collab), trailing only on PGP where COPRA reaches 0.783 compared with 0.68 for ACO-CNoD. Together, these contributions establish a new methodological foundation for community detection, offering complementary approaches for different network types and application requirements. The research balances theoretical advancement with practical applicability, bridging fundamental graph theory with real-world applications in social media analysis, biological networks, organisational studies, and infrastructure optimisation. The integrated framework significantly enhances our ability to extract meaningful community structures from complex networks, with implications for diverse domains including recommendation systems, influence maximisation, and network resilience analysis.