(a) An example of a weighted network where thresholding will never succeed. (b) A plot of the normalized mutual information (NMI) between the true community structure and inferred SBM community structure after thresholding at various threshold values (averaged over 100 trials). Examples of community structure found by thresholding are shown above the graph (different shades of gray). As the NMI is |$<$|1 for all threshold values, the SBM after thresholding never infers the true community structure shown in (a).