Backbone extraction through statistical edge filtering: A comparative study.

The backbone extraction process is pivotal in expediting analysis and enhancing visualization in network applications. This study systematically compares seven influential statistical hypothesis-testing backbone edge filtering methods (Disparity Filter (DF), Polya Urn Filter (PF), Marginal Likelihood Filter (MLF), Noise Corrected (NC), Enhanced Configuration Model Filter (ECM), Global Statistical Significance Filter (GloSS), and Locally Adaptive Network Sparsification Filter (LANS)) across diverse networks. A similarity analysis reveals that backbones extracted with the ECM and DF filters exhibit minimal overlap with backbones derived from their alternatives. Interestingly, ordering the other methods from GloSS to NC, PF, LANS, and MLF, we observe that each method's output encapsulates the backbone of the previous one. Correlation analysis between edge features (weight, degree, betweenness) and the test significance level reveals that the DF and LANS filters favor high-weighted edges while ECM assigns them lower significance to edges with high degrees. Furthermore, the results suggest a limited influence of the edge betweenness on the filtering process. The backbones global properties analysis (edge fraction, node fraction, weight fraction, weight entropy, reachability, number of components, and transitivity) identifies three typical behavior types for each property. Notably, the LANS filter preserves all nodes and weight entropy. In contrast, DF, PF, ECM, and GloSS significantly reduce network size. The MLF, NC, and ECM filters preserve network connectivity and weight entropy. Distribution analysis highlights the PU filter's ability to capture the original weight distribution. NC filter closely exhibits a similar capability. NC and MLF filters excel for degree distribution. These insights offer valuable guidance for selecting appropriate backbone extraction methods based on specific properties.