Fig. 2

Filter performance on synthetic networks. Network filter tests on synthetic graphs with varying structures and known noise. The Mean Absolute Error (MAE) of a network filters, b Laplacian exponential diffusion kernel, and c netSmooth on the permuted nodes as a function of the assortativty coefficient of 5000 instances of noisy non-modular graphs. The smooth filters (mean and median) perform best on assortative data (\(r>0\)), while the sharp filter is optimal for disassortative data (\(r<0\)). When data are neither assortative nor disassortative (\(r \approx 0\)), netSmooth and Laplacian exponential kernels perform best. The MAE of d network filters, e Laplacian exponential diffusion kernel, and f netSmooth on the permuted nodes as a function of the fraction of communities with assortative data values for 100 instances of noisy modular graphs. Each network instance has 5 communities and we vary how many communities have assortative versus disassortative data values with a moderate assortativity coefficient \(|r|\in [0.4,0.7]\). The shaded areas indicate 99% bootstrapped confidence intervals