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The observed gene maximum multiplicity values for each gene ranged from 1 to 23.
The observed gene maximum multiplicity values for each cluster range from 1.0 to 10.3 (see Figure 3).
The average cancer maximum multiplicity values for clusters 1, 2, and 3 are 14.5, 8.11, and 26.5, respectively.
The ranks of the average of the cancer maximum multiplicity values for clusters are significantly different via a Kruskal-Wallis test (H = 16.98, df = 2, p < 0.05).
There is a strong positive correlation between average gene maximum multiplicity values for clusters and number of causal genes per cluster (r s 8) = 0.894, Spearman's t = 17.48, p < 0.05).
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Additional File 2 provides a gene maximum multiplicity value for each gene.
Median multiplicity value for clusters 1, 2, and 3 are 15, 10, and 45, respectively.
Similar to Experiment 1 for gene maximum multiplicity, the cancer maximum multiplicity value for a cancer type is obtained from its maximum value link to any cancer type in the graph.
For both proteins, there was a noticeable shift toward higher multiplicity values from round 3 to round 5.
The maximum multiplicity values are reversed for genes, with early causal genes having higher multiplicity values, indicating that early causal genes are systemic across cancers.
For example in Figure 1, a gene maximum multiplicity value of 2 is listed inside all the nodes since each node has a maximum multiplicity link of magnitude 2. Specifically, gene maximum multiplicity (Eq. 1, GeneMaxMultiplicity) and gene link multiplicity (Eq. 2, GeneLinkMultiplicity) are defined as follows.
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