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