Generalized walks-based centrality measures for complex biological networks

Abstract

A strategy for zooming in and out the topological environment of a node in a complex network is developed. This approach is applied here to generalize the subgraph centrality of nodes in complex networks. In this case the zooming in strategy is based on the use of some known matrix functions which allow focusing locally on the environment of a node. When a zooming out strategy is applied new matrix functions are introduced, which give a more global picture of the topological surrounds of a node. These indices permit a modulation of the scales at which the environment of a node influences its centrality. We apply them to the study of 10 protein-protein interaction (PPI) networks. We illustrate the similarities and differences between the generalized subgraph centrality indices as well as among them and some classical centrality measures. We show here that the use of centrality indices based on the zooming in strategy identifies a larger number of essential proteins in the yeast PPI network than any of the other centrality measures studied.

Milestones in graphical bioinformatics

“…Those interested in complex networks, including protein interaction networks, and their analysis should consult several papers of Estrada and colleagues as a good introduction in this topic. [125,[153][154][155][156][157][158][159][160][161][162][163][164][165][166][167] Table 25 shows that research in China in graphical bioinformatics has deep roots, and it appears that China will soon, if not already, be the leading country in the development of graphical bioinformatics. In China, the dominant groups of researchers come from mathematical institutions, and they are interested in discrete mathematics and graph theory.…”

Some New Properties for Degree-Based Graph Entropies

“…The degree powers are extremely significant invariants and studied extensively in graph theory and network science, and they are used as the information functionals to explore the networks [12,13]. For more expansive research, Estrada and co-authors proposed a physically-sound entropy measure for networks/graphs [14] and studied the walk-based graph entropies [15][16][17]. There is am especially close relationship between the graph entropies based on length-two cycles and the graph entropies based on the degree powers for exponent k = 1.…”

Scale-space measures for graph topology link protein network architecture to function

“…Measures that characterize ‘meso-scale’ topology have been proposed before (Jordán and Scheuring, 2002; Winterbach et al , 2013b). Of particular interest is the scale-aware version of the subgraph centrality, proposed by Estrada, that resulted in superior ability to identify essential proteins (Estrada, 2010). However, the method used to incorporate scale does not extend to other topological measures and, moreover, was discrete in nature.…”