S 1 : Methods description and relationships between module preservation statistics

Here, we provide additional methodological details regarding the module preservation statistics. In the first section, we describe standard cross-tabulation based module preservation statistics. Specifically, we present three basic crosstabulation based statistics for determining whether modules in a reference data set are preserved in a test data set. These statistics do not assume that a test network is available. Instead, module assignments in both the reference and the test networks are needed. In the second section, we briefly review a hierarchical clustering procedure for module detection. Many methods exist for defining network modules. In this section, we describe the method used in our applications but it is worth repeating that our preservation statistics apply to most alternative module detection procedures. In the third section, we review the definition of signed and unsigned correlation networks. Correlation networks are a special case of general undirected networks in which the adjacency is constructed on the basis of correlations between quantitative variables. In the fourth section, we present module quality statistics that we are implemented in the modulePreservation R function. While our main article focuses on statistics that measure preservation of modules between a reference and a test network, we briefly discuss the application of some of the preservation statistics to the related but distinct task of measuring module quality in a single (reference) network. More precisely, the density and separability statistics can be applied to the reference network without a reference to a test network. The results can then be interpreted as measuring module quality, that is how closely interconnected the nodes of a module are or how well a module is separated from other modules in the network. In the fifth section, we review the notation for the singular value decomposition and for defining a module eigennnode. The section describes conditions when the eigenvector E is an optimal way of representing a correlation module. It also reviews the definition of propVarExpl (the proportion of the variance explained by the eigennode). We derive a relationship between propVarExpl and the module membership measures kME , which will be useful for deriving relationships between preservation statistics. In the sixth section, we investigate relationships between preservation statistics in correlation networks. An advantage of an (unsigned) weighted correlation network is that it allows one to derive simple relationships between network concepts [1, 2]. We characterize correlation modules where simple relationships exist between i) density-based preservation statistics, ii) connectivity based preservation statistics, and iii) separability based preservation statistics. Apart from studying relationships among preservation statistics in correlation networks, we also briefly describe relationships between preservation statistics in general networks. In the seventh section we briefly review the In-Group Proportion method [3].