Topological Invariants, Centrality Asymmetry, and Complex Contagion in Federated Social Networks: A Directed Graph Structural Analysis

Decentralized social architectures and federated media ecosystems distribute content syndication and administrative authority across autonomous server instances. The research investigates structural stratification, directional prestige asymmetry, and complex contagion dynamics within open federated networks. The investigation executes an empirical eleven-stage pipeline combining microscopic centrality formulations, Wasserman-Faust prestige metrics, Kleinberg spectral decomposition, Clauset maximum-likelihood power-law estimation, small-world benchmarking, topological link prediction heuristics, Granovetter behavioral threshold modeling, and discrete Markov random walk simulations on a directed graph of 1,553 instances and 43,879 links.Empirical degree sequences follow a scale-free power law with scaling exponent alpha equal to 2.6028, while the network exhibits small-world organization with coefficient sigma equal to 24.52. Preferential attachment achieves an area under the curve of 0.9767 in link prediction, while resource allocation attains perfect precision across the top one hundred predictions. Targeted seeding of the top eight percent of instances by PageRank precipitates a global cascade reaching 97.6 percent adoption, whereas uniform random seeding requires twenty percent penetration. Random walk visit frequencies converge ergodically to theoretical PageRank stationary probabilities, decreasing total variation distance to 0.0