Fig. 4

Realisations from a block-constrained configuration model obtained by fixing the out-degree distribution and varying the parameters within the block-matrix B. Each realisation is obtained from a BCCM with N=50 vertices and m=500 directed edges. The out-degree distribution of the vertices in each block follows a power-law distribution with parameter α=1.8 The vertices are separated into 5 equally sized blocks and the structure of the block-matrix B is given by Eq. 10, but in each graph the values of some of the parameters \(\omega _{b_{i}b_{j}}\) are changed. On left side, a is a realisation from a BCCM where the between-block parameters are increased to 1. In the center, b is a realisation obtained by increasing the parameter \(\omega _{b_{1}}\) that controls for the internal cohesion of the first block. On the right side, c is a realisation obtained by increasing to 0.8 the between-block parameters \(\omega _{b_{1}b_{2}}, \omega _{b_{3}b_{4}}\), and \(\omega _{b_{4}b_{5}}\), to create a hierarchical block structure where the first two blocks are part of a macro cluster, and the last three blocks are part of another. All graphs are visualised using the force-atlas2 layout with weighted edges. Out-degrees determine vertex sizes, and edge widths the edge counts