Network histograms and universality of blockmodel approximation

Representing and understanding large networks remains a major challenge across the sciences, with a strong focus on communities: groups of network nodes whose connectivity properties are similar. Here we argue that, independently of the presence or absence of actual communities in the data, this notion leads to something stronger: a histogram representation, in which blocks of network edges that result from community groupings can be interpreted as two-dimensional histogram bins. We provide an automatic procedure to determine bin widths for any given network and illustrate our methodology using two publicly available network datasets.