Centered ellipsoid fitting of m Gaussian points in R^d has a sharp phase transition at m = (1 ± o_d(1)) d^2/4.
Spectral redemption in clustering s parse networks
5 Pith papers cite this work, alongside 657 external citations. Polarity classification is still indexing.
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HOPPER learns graph- and hop-adaptive sequence extraction for linearized graph sequence models, recovering fixed LGSM extractors as special cases and achieving the best reported scores on eccentricity and shortest-path prediction in ECHO-SYNTH.
Sparse Erdős-Rényi graphs of average degree d have vector chromatic number (1/2)√d + o_d(1).
Strong local community structure, caused by population-driven clustering of nodes, reduces the robustness of planar spatial networks against node-removal attacks.
A literature survey that proposes a multidimensional taxonomy for community detection, introduces a general mathematical formalization accommodating disjoint/overlapping/fuzzy structures, reviews modularity functions and both algorithmic and mathematical programming methods, and discusses benchmark
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Vector Colorings of Random, Ramanujan, and Large-Girth Irregular Graphs
Sparse Erdős-Rényi graphs of average degree d have vector chromatic number (1/2)√d + o_d(1).