Maximum entropy filtering of weighted networks

Abstract

The increasing availability of data of large-scale complex systems has resulted in noisy and extremely dense complex networks, reducing their sparsity that constitutes one of the hallmarks of complex networks, making them more difficult to interpret, visualize andZ study from a computational perspective. Network filtering responds to the necessity to continue using the toolbox of network science to analyze larger networks, and several methods and approaches exist deal with this problem, focusing on extracting the so-called backbone of a given network, which is a sparsesubgraph retaining some properties of the original network. The properties a backbone retains from its ancestor network will depend on the method used to retrieve it. We study backbone extraction with the Enhanced Configuration Model (ECM) filter, a maximum-entropy approach that shares the advantages of some existing filtering techniques, while solving some of their problems. Remarkably, the ECM-filter is an unbiased approach that preserves the degree and strength distribution. First, we have performed a systematic benchmark of the ECM-filter using synthetic networks topologies with a known backbone. We have found that an optimal acceptance level can be identified for which the extracted backbone is the most alike possible to the expected, synthetic, one. Also, we notice that such acceptance level scales with the network size as a power-law. Then, we have studied how the properties of real complex networks vary as they are filtered with the ECM-filter. We have found that even if there is no universal behavior shared by the empirical networks considered, the ECMfilter consistently extracts non trivial and well connected backbones comprising a major part of the nodes even when a significant fraction of the edges are already pruned. We discuss the different criteria that can be used to choose a suitable acceptance value for the ECM-filter depending on the type of structure and properties we want the extracted backbone to have