The triplet with a single connection or “directed edge” (pattern 2) is weakly underrepresented (ratio = 0.7 for both uniform and nonuniform random models; p = 0.0016 and 0.0064, respectively), the triplet with diverging connections or “V-out” (pattern 4) is overrepresented (ratio = 2.2 and 2.3 for the uniform and nonuniform random models; p = 0.043 and 0.022, respectively). The “feedforward” (pattern 10) is highly overrepresented (ratio = 3.2 and 3.5; p = 0.014

and 0.002, respectively). Transitivity means that if there is a connection from cell A to cell B, and from cell B to cell C, there will also be a connection from A to C. Because a preference for transitive connectivity has been reported in other complex networks (Holland and Leinhardt, 1970 and Milo et al., 2004), we tested this

hypothesis in the MLI network and therefore grouped the patterns according to their property of transitivity (Bang-Jensen and Gutin, 2008; Supplemental Experimental Procedures; Figure S5A). Capmatinib in vivo check details Indeed, we found that intransitive patterns tend not to be observed in the data (e.g., the “three-loop” pattern 11, and the “mutual in” pattern 7), or appear to be underrepresented (the “three-chain” pattern 6, ratio = 0.5 compared to prediction of the nonuniform random model), whereas transitive patterns (e.g., the feedforward pattern 10, and the “regulating mutual” pattern 14) tend to be overrepresented (ratio = 3.5 and 6.3 compared to the prediction of the nonuniform random model). We therefore divided the observed patterns into two groups: transitive

and intransitive. By this definition, patterns 10, 12, 14, 16 are transitive, and patterns 6, 7, 8, 9, 11, 13, 15 are intransitive (Figure 5A). Patterns 1, 2, 3, 4, 5 are excluded, as the property is not applicable due to the low number of connections. We observed significantly more transitive and significantly fewer intransitive patterns compared to both predictions (Figure 5B; uniform random: p = 0.0001 and 0.0016, respectively; nonuniform random: p = 0.0001 and 0.0026, respectively). This result highlights that random connectivity models are not sufficient to describe the connectivity of the MLI network, in the particular, with respect to their transitive property. To confirm the large deviation of the data compared to both models, we next calculated the average chemical clustering coefficient CC and anticlustering coefficient ACC for triplets and quadruplets, treating bidirectional and unidirectional connections identically. We observed a higher clustering coefficient CC in the data than predicted by both random connectivity models ( Figure 5C; p = 0.0020 and 0.0023, respectively). The values of CC for the uniform random and nonuniform random predictions are similar due to the weak distance dependence of the probability of chemical connections ( Figures 2A, 2B, and S2). We also found that ACC was not correctly predicted by the random connectivity models ( Figure 5C; p = 0.0012 and 0.0028, respectively).