  Methods for determining the percolation threshold usually study the behavior
of network ensembles and are often restricted to a particular type of
probabilistic node/link removal strategy. We propose a network-specific method
to determine the connectivity of nodes below the percolation threshold and
offer an estimate to the percolation threshold in networks with bidirectional
links. Our analysis does not require the assumption that a network belongs to a
specific ensemble and can at the same time easily handle arbitrary removal
strategies (previously an open problem for undirected networks). In validating
our analysis, we find that it predicts the effects of many known complex
structures (e.g., degree correlations) and may be used to study both
probabilistic and deterministic attacks.
