General Network Models with Transitive Structures
summary
Proposes TIER (Transitive Inhomogeneous Erdos-Renyi) models that repeatedly perform triangle closure and empirically produce all five desired features: sparsity, small‑world distances, community structure, power‑law degrees and high triangle counts, with eigengaps increasing as tiers accumulate. Proves spectral concentration for aggregated adjacency and Laplacian under a lazy temporal model, deriving a rate proportional to 1/sqrt(1-alpha) via a geometric random variable argument. Uses spectral clustering, squared adjacency with diagonal removal and degree thresholding for community recovery, and a Q‑sum change‑point statistic, with simulation errors growing as alpha increases.
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chapters (7)
- 0:00Introduction to network data
- 2:07Evolution of network models
- 6:54Multi-layer network framework
- 12:24Dependence in adjacency matrices
- 25:17Parameter-based dependencies
- 33:29Triangle closure and properties
- 38:16Discussion and Q&A
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