4 research outputs found
Size reduction of complex networks preserving modularity
The ubiquity of modular structure in real-world complex networks is being the
focus of attention in many trials to understand the interplay between network
topology and functionality. The best approaches to the identification of
modular structure are based on the optimization of a quality function known as
modularity. However this optimization is a hard task provided that the
computational complexity of the problem is in the NP-hard class. Here we
propose an exact method for reducing the size of weighted (directed and
undirected) complex networks while maintaining invariant its modularity. This
size reduction allows the heuristic algorithms that optimize modularity for a
better exploration of the modularity landscape. We compare the modularity
obtained in several real complex-networks by using the Extremal Optimization
algorithm, before and after the size reduction, showing the improvement
obtained. We speculate that the proposed analytical size reduction could be
extended to an exact coarse graining of the network in the scope of real-space
renormalization.Comment: 14 pages, 2 figure
Fast unfolding of communities in large networks
We propose a simple method to extract the community structure of large
networks. Our method is a heuristic method that is based on modularity
optimization. It is shown to outperform all other known community detection
method in terms of computation time. Moreover, the quality of the communities
detected is very good, as measured by the so-called modularity. This is shown
first by identifying language communities in a Belgian mobile phone network of
2.6 million customers and by analyzing a web graph of 118 million nodes and
more than one billion links. The accuracy of our algorithm is also verified on
ad-hoc modular networks. .Comment: 6 pages, 5 figures, 1 table; new version with new figures in order to
clarify our method, where we look more carefully at the role played by the
ordering of the nodes and where we compare our method with that of Wakita and
Tsurum