Extracting backbones in weighted modular complex networks.

Network science provides effective tools to model and analyze complex systems. However, the increasing size of real-world networks becomes a major hurdle in order to understand their structure and topological features. Therefore, mapping the original network into a smaller one while preserving its information is an important issue. Extracting the so-called backbone of a network is a very challenging problem that is generally handled either by coarse-graining or filter-based methods. Coarse-graining methods reduce the network size by grouping similar nodes, while filter-based methods prune the network by discarding nodes or edges based on a statistical property. In this paper, we propose and investigate two filter-based methods exploiting the overlapping community structure in order to extract the backbone in weighted networks. Indeed, highly connected nodes (hubs) and overlapping nodes are at the heart of the network. In the first method, called "overlapping nodes ego backbone", the backbone is formed simply from the set of overlapping nodes and their neighbors. In the second method, called "overlapping nodes and hubs backbone", the backbone is formed from the set of overlapping nodes and the hubs. For both methods, the links with the lowest weights are removed from the network as long as a backbone with a single connected component is preserved. Experiments have been performed on real-world weighted networks originating from various domains (social, co-appearance, collaboration, biological, and technological) and different sizes. Results show that both backbone extraction methods are quite similar. Furthermore, comparison with the most influential alternative filtering method demonstrates the greater ability of the proposed backbones extraction methods to uncover the most relevant parts of the network.