Fig. 5

Local structure of top contributing nodes (TCNs). Left panel denotes the local structure of all TCNs in the disease network whereas right panel denotes the local structure for the same proteins in the normal network. Yellow represents TCNs and pink represent their first neighbor. The TCNs, in addition to the functional importance pertaining to the occurrence of the disease state revealed, exhibits interesting structural properties. This is more remarkable in the light that all of these TCNs lie in the low degree regime in the networks. Moreover, their betweenness centrality also are zero further ruling out any trivial structural significance of these nodes. But importance of these nodes based on the analysis of their interactions reveals the existence of preserved local structural patterns. Most strikingly, all of them follow phenomenon of gene duplication which shows TCNs being involved in the pair formation in which first node in each pair has exactly the same neighbors as of the second node. Most remarkably, there are 20 duplicates (proteins having the same number of neighbors and having more than one connection) in the whole network of which 18 are found in the TCNs of the most localized eigenvectors (Rai et al. 2014)