Fig. 4

Benchmark patterns for DeRegNet and Backes et al. [40]. A Distributions of the Matthews correlation coefficients of DeRegNet and Backes et al. subgraphs. B Distributions of the F1 scores of DeRegNet and Backes et al. subgraphs. C Distributions of the Jaccard indices of DeRegNet and Backes et al. subgraphs. D Running time (in s) of DeRegNet (Dinkelbach algorithm) and \(k_{max} - k_{min} + 1\) (\(k_{max} = 50\), \(k_{min} = 25\)) runs of the Backes et al. algorithm [40]. Benchmark parameters: in-subgraph deregulation probability \(p'=0.99\), out-of-subgraph deregulation probability \(p = 0.01\), \(k_{min} = 25\), \(k_{max} = 50\), minimal size of simulated true subgraph \(=30\), maximal size of simulated true subgraph \(=45\), number of simulated instances \(=100\), time limit \(=600\) s. See Additional file 1: Supplementary Material and Methods for further formal details on the simulation procedure and Additional file 2: Figs. S18–S24 for simulation results for different parameter value settings