Distribution of mutual information for different lengths of the shortest path between genes for the scale-free topology. Here we plot the log of the empirical probability that MI for a given separation between genes is above some value (in nats) marked on the horizontal axis. High MI values are significantly more probable for closer genes. Statistical significance threshold of 10-4 for the background MI distribution, corresponding to I0 = 0.0175 nats, is marked on the graph. As shown, this threshold retains a large number of indirect candidate interactions, and there is no threshold that would be able to separate indirect and direct interactions; a threshold that eliminates most of the former (red arrows) also eliminates the majority of the latter. This severely degrades performance of RNs. (Inset) Expanded log-log view of the MI distribution for 934 gene pairs with 3 or more intermediaries and the background distribution computed by Monte Carlo. The curves are virtually indistinguishable, indicating that the background distribution can be used to obtain reliable estimates of statistical significance thresholds for filtering genes with higher degrees of connectivity. Similar results apply for the Erdös-Rényi topology (see additional file 3: MI distribution for different shortest path lengths for the Erdös-Rényi topology).