A network-specific approach to percolation in complex networks with bidirectional links

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.