  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.
