Social Network Analysis (SNA) is a powerful interdisciplinary field that explores the patterns and dynamics of relationships between individuals, groups, organizations, and even entire societies. This article provides an overview of SNA, tracing its roots in graph theory and highlighting its various applications in fields such as sociology, computer science, business, and epidemiology. By examining the theoretical foundations of SNA and its practical implementations, this article aims to demonstrate the importance of SNA in understanding social structures, information diffusion, impact dynamics, and collective behavior. In addition, the article discusses the methodologies and tools used in SNA research, including data collection, network visualization and network metrics. Through a comprehensive analysis of SNA techniques and their applications, this article contributes to the growing knowledge in the analysis of social networks and encourages further exploration of this rich field.

This paper presents an integrated approach to social network analysis that combines graph theory, social network analysis (SNA), and Shannon’s information theory, applied to a real-world Twitter network built around the political hashtag Zandberg. Unlike studies based on synthetic data, our analysis leverages empirical content from a live political discourse. We employ classical centrality measures (degree, betweenness, closeness), local clustering coefficients, and community detection using the Louvain algorithm. A key theoretical contribution is the introduction of a novel metric: the Structural Entropy Index of a Community (SEIC), which quantifies internal decentralization of communication independently of community size. The analysis reveals significant variation in community structures and entropy levels. Larger communities tend to be decentralized (SEIC > 0.8), while smaller groups are often dominated by single influential nodes. These findings have practical implications for influencer identification, disinformation resilience assessment, and communication strategy optimization. The proposed methodological framework provides a robust tool for studying the structural and informational dynamics of real-world social networks in digital environments.

The rapid expansion of digital communication during politically sensitive events, such as the 2020 U.S. presidential election, has created networks of unprecedented complexity. Traditional approaches based on classical graph theory and random walks are often insufficient to explain nonlinear diffusion patterns, overlapping narratives, and the sudden synchronization of distant communities. This study intro- duces Quantum Graph Theory (QGT) as a novel framework for analyzing online communication networks. Drawing on concepts from quantum information science, including continuous-time quantum walks, von Neumann entropy, and entanglement, we analyze Twitter/X interaction data collected across three periods: pre- election (October 20 – November 2, 2020), election night (November 3–4, 2020), and post-election (November 5–10, 2020). The results demonstrate that quantum- walk centrality identifies hidden influencers not detected by PageRank, von Neumann entropy captures systemic transitions from ordered to chaotic communication, and entanglement proxies reveal coordinated clusters involved in the dissemination of disinformation. By bridging quantum theory and network analysis, the paper presents Quantum Graph Theory as both a theoretical extension and a practical methodology for the study of contemporary social communication.

Communication networks can reorganize before those changes become visible in message volume. This article introduces Entropy Dynamics, a prospective framework that represents rolling communication windows as reuse-based proxy graphs and monitors changes in von Neumann graph entropy under limited observability. The approach is evaluated on two 2017 Twitter corpora associated with the Internet Research Agency (IRA), for which complete source–target diffusion links are unavailable. In the sparse October 2017 stream, the method detects concentration changes with recall of 0.958 using 9 alerts, 0.163 false alarms per day, and a median lead time of 50 hours. A Shannon-entropy baseline reaches recall of 1.000 but requires 33 alerts and provides a shorter median lead time of 12 hours. In the denser August 2017 stream, von Neumann entropy retains meaningful recall but loses most of its lead-time advantage, while simpler baselines become competitive. The results support a bounded conclusion: entropy-based monitoring is most useful in sparse reuse streams where structural compression precedes volume escalation. The article contributes (1) a prospective entropy-monitoring protocol with no future leakage, (2) an Operating Conditions Framework that links observable stream properties to expected method strengths, and (3) a proposed two-layer monitoring architecture that combines an always-available throughput–recurrence gatekeeper with a conditional entropy monitor. The gatekeeper remains to be validated empirically.