Spectral bounds for percolation on directed and undirected graphs
Kathleen E. Hamilton, Leonid P. Pryadko
TL;DR
This paper develops algebraic bounds to analyze percolation phenomena on both directed and undirected graphs, focusing on cluster proliferation and phase transitions.
Contribution
It introduces new algebraic bounds for understanding percolation thresholds and cluster growth in complex networks, applicable to directed and undirected graphs.
Findings
Bounds for strongly-connected cluster proliferation
Bounds for in- and out-cluster proliferation
Insights into phase transitions and giant component emergence
Abstract
We give several algebraic bounds for percolation on directed and undirected graphs: proliferation of strongly-connected clusters, proliferation of in- and out-clusters, and the transition associated with the number of giant components.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Graph theory and applications · Random Matrices and Applications