@article{eb91e55661e9444ab162a401742c4530,
title = "Algebraic bounds for heterogeneous site percolation on directed and undirected graphs",
abstract = "We analyze site percolation on directed and undirected graphs with site-dependent open-site probabilities. We construct upper bounds on cluster susceptibilities, vertex connectivity functions, and the expected number of simple open cycles through a chosen arc; separate bounds are given on finite and infinite (di)graphs. These produce lower bounds for percolation and uniqueness transitions in infinite (di)graphs, and for the formation of a giant component in finite (di)graphs. The bounds are formulated in terms of appropriately weighted adjacency and non-backtracking (Hashimoto) matrices. It turns out to be the uniqueness criterion that is most closely associated with an asymptotically vanishing probability of forming a giant strongly-connected component on a large finite (di)graph.",
keywords = "Digraph, Infinite graph, Non-backtracking spectra, Percolation, Vertex connectivity",
author = "Hamilton, {Kathleen E.} and Pryadko, {Leonid P.}",
note = "Publisher Copyright: {\textcopyright} 2017 Elsevier B.V.",
year = "2017",
month = may,
day = "11",
doi = "10.1016/j.dam.2016.12.027",
language = "English",
volume = "222",
pages = "124--142",
journal = "Discrete Applied Mathematics",
issn = "0166-218X",
publisher = "Elsevier",
}