Gene regulatory network associated with proliferation in primary breast cancer after DPI pruning of indirect interactions. Panel A depicts the Breast Cancer associated GRN (Baca-López et al. 2012) (same as in Figure 4)after eliminating all indirect interactions by means of the application of the Data Processing Inequality (DPI). The relative importance of highly connected genes is now more evident. The network is basically founded on the role of two major hubs (that are also connected by means of intermediate nodes) and a couple of medium-high connected nodes. Panel B depicts the same network, nodes are size-coded and color-coded according with their connectivity degree. Two major hubs appear corresponding to MEF2C (red node) and MNDA (dark orange node). These two genes have been recognized as transcriptional master regulators in breast cancer (Baca-López et al. 2012). In panel C we can see the connectivity degree distribution that now resembles a power law distribution (too few nodes, however to have a reliable statistic for the fit) indicating a relatively high importance of few nodes and a low importance for most nodes. In panel D we can see how the average clustering coefficient has drop to zero. This is a clear effect of pruning for indirect interactions, since the relative importance of a node is now given in terms of its direct connections and not because of neighbor-by-neighbor influence. Panel E presents the short path length distribution that again is a bimodal (with maxima at the same distances of 2 and 4 links) that however shows a somehow larger tail than in Figure 4. This may be due to the fact that navigability in the network was easier in the presence of indirect interactions.