Analyses of antigen dependency networks unveil immune system reorganization between birth and adulthood

Much effort has been devoted to assess the importance of nodes in complex biological networks (such as gene transcriptional regulatory networks, protein interaction networks, and neural networks). Examples of commonly used measures of node importance include node degree, node centrality, and node vulnerability score (the effect of the node deletion on the network efficiency). Here, we present a new approach to compute and investigate the mutual dependencies between network nodes from the matrices of node-node correlations. To this end, we first define the dependency of node i on node j (or the influence of node j on node i), D(i, j) as the average over all nodes k of the difference between the i − k correlation and the partial correlations between these nodes with respect to node j. Note that the dependencies, D(i, j) define a directed weighted matrix, since, in general, D(i, j) differs from D( j, i). For this reason, many of the commonly used measures of node importance, such as node centrality, cannot b...