Soft Trioid Graphs for Dynamic Social Network Analysis

Abstract

Soft trioid graphs integrate parameterized algebra with graph theory to model systems exhibiting both algebraic structure and relational connectivity under varying contexts. This paper applies the framework to dynamic social network analysis, demonstrating that semilattice decomposition of an idempotent network yields temporally stable com-munities, with idempotent elements serving as persistent influencers. Empirical valida-tion on Twitter data achieves 92% agreement with ground-truth community annotations, substantially outperforming traditional methods such as Louvain (0.62), Infomap (0.65) and dynamic stochastic block models (0.71). The decomposition further reveals hier-archical influence structures, with top-tier influencers exhibiting slow influence decay. These findings establish soft trioid graphs as a robust mathematical tool for analyzing parameterized relational systems across scientific and engineering domains.