2 research outputs found
A network-specific approach to percolation in 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.Comment: 6 pages, 8 figure
Detecting the overlapping and hierarchical community structure of complex networks
Many networks in nature, society and technology are characterized by a
mesoscopic level of organization, with groups of nodes forming tightly
connected units, called communities or modules, that are only weakly linked to
each other. Uncovering this community structure is one of the most important
problems in the field of complex networks. Networks often show a hierarchical
organization, with communities embedded within other communities; moreover,
nodes can be shared between different communities. Here we present the first
algorithm that finds both overlapping communities and the hierarchical
structure. The method is based on the local optimization of a fitness function.
Community structure is revealed by peaks in the fitness histogram. The
resolution can be tuned by a parameter enabling to investigate different
hierarchical levels of organization. Tests on real and artificial networks give
excellent results.Comment: 20 pages, 8 figures. Final version published on New Journal of
Physic