Extensive discussion has occurred among the authors regarding weight definition for this analysis. Although the most obvious approach is to add or multiply the normalized expression values of cognate molecules in the respective clusters of each edge, such an approach has a number of problems that were considered for this study. First, to do so would obscure the relevance of signaling molecules transcribed at low levels but which are highly specific to certain clusters. Second, variable transcript quality and capture rate make comparing normalized expression levels inappropriate across batches. We therefore defined the weight of an edge as the sum of the z scores (scaled expression) of cognate molecules in the respective clusters of each edge. This approach rewards outliers within a given batch, at the cost of penalizing molecules that are pan-expressed across the entire cell population. This bears on interpretation of the results in this study, because a strong score reflects the observation that a node tended to be an outlying producer of molecules within the set being tested, some of which may be expressed at very low levels (such as WNTs).

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