Information-Theoretic Thresholds for Planted Dense Cycles

We study a random graph model for small-world networks which are ubiquitous in social and biological sciences. In this model, a dense cycle of expected bandwidth $n \tau$, representing the hidden one-dimensional geometry of vertices, is planted in an ambient random graph on $n$ vertices. For both detection and recovery of the planted dense cycle, we characterize the information-theoretic thresholds in terms of $n$, $\tau$, and an edge-wise signal-to-noise ratio $\lambda$. In particular, the information-theoretic thresholds differ from the computational …

ambient bandwidth biological sciences cs.it cs.si detection geometry graph hidden information math.it math.st networks random recovery small social stat.ml stat.th study world