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Finally, binary interaction networks are constructed by a simple thresholding method.

The inferred binary interaction networks are sparse and modular, which agree with our intuition for the networks of direct physical interactions with protein complexes [ 13].

Based on the current view on binary interaction networks that hubs tend to be more essential than non-hub proteins [ 22- 25], one would expect the fraction of essential genes which are present in many complexes to be significantly higher than the fraction of inessential genes.

Moreover, standard measures of gene centrality focus on binary interaction networks, which may not always be suitable in the context of co-expression networks.

We then use these two cutoffs to construct the binary interaction networks (Fig. 1 d).

The reconstructed interaction network was integrated into a novel visualization mode named the Binary Matrix.

Protein interaction network was compiled from studies of Krogan et al (2006) [13] (high quality binary interaction data) and Bader et al (2004) [12] (high quality interactions with a confidence cut-off of 0.65).

To construct a comprehensive binary interaction network, we rank the observed co-complex interactions according to their BINM scores and predict the top-ranked interactions as binary interactions.

Since modules must contain dense submodules, we first identified all four-cliques in a degenerated binary interaction network.

Unlike expression data for which we have correlation measurement for each edge leading to a unique score for each interaction, PPI networks are binary and result in a unique score for all interactions in each of the species (see Additional File 1 Supplementary Methods).

Binary networks are simpler to collect and analyze.