Graph-theoretic and geometric methods for social network influence analysis

The growing role we play in influencing and being influenced by those around us, for better or worse, underscores the importance of having proven ways to analyze and model the propagation of influence. The use of such techniques or traditional graph theoretic approaches alone do not capture the complex, non-linear nature of many real-world social networks. In response to this problem, in this paper we present a new framework combining graph and geometry approaches for full analysis of social network influence. We mix traditional centrality statistics like degree, betweenness, clustering coefficients, with more sophisticated lower-level geometric features, such as geodesics and curvature analysis obtained at the price of using Riemannian geometry. This Hybrid model also allows us to infer the key players who provide us with further detailed information about the structural strength and interaction of a network. Drawing on geometric characteristics, our approach successfully captures correlation of nonlinear effect, resulting in more accurate influence spread estimation. We use the real-world social network data to conduct a case study and show that the proposed framework not only enhances the effectiveness of critical node-oriented attacks in target identification but also leads to a more accurate discovery of bottlenecks and weakly connected regions. The presented method alleviates the difficulties of the established techniques by providing a mathematically structured, yet computationally efficient framework that provides interpretability offered from graph theory with the level of detail from geometric analysis. This work can inform targeted marketing, misinformation control and community behavior dynamics, and lends novel insights to the study of influence dynamics in social networks more broadly.