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A comparative performance analysis of the exponential-based and resolvent-based centrality measures

Wilczek Piotr

Silesian Journal of Pure and Applied Mathematics

2020

vol. 10, iss. 1

45--102

The present study aims to quantitatively assess the effect of the attenuation factor on the resolution, performance, rank correlations, robustness and assortativity of the Katz centrality measure. We found that the granularity of the exponential-based and resolvent-based ranking algorithms is strongly correlated with the number of automorphically equivalent nodes within the network. Thus, this result can be viewed as a bridge between algebraic and quantitative graph theory. Moreover, we substituted the dichotomous adjacency matrix in the definitions of the exponential-based and resolvent-based centrality indices by its weighted (normalized) version and, therefore, we obtained two novel ranking algorithms. The deliberate attack simulation experiments carried out on four empirical and on two model networks showcased that the newly suggested ranking methods considerably outperform their unweighted counterparts as well as the classical degree centrality measure. In the last part of the paper, we introduced the concept of the centrality assortativity profile of a complex network. The extensive numerical results demonstrated that this novel theoretical notion is useful in complex network mining.

Identifying influential nodes in the genome-scale metabolic networks

Wilczek Piotr

Silesian Journal of Pure and Applied Mathematics

2019

vol. 9, iss. 1

9--47

The present article introduces two novel centrality indices which can be used in order to characterize the genome-scale metabolic networks. The deliberate attack simulation experiments conducted on two Barab´asi-Albert models and four genome-scale metabolic networks demonstrate that the proposed ranking methods are effective in identifying essential nodes in complex networks. Also, the Principal Component Analysis reveals that the Kendall centrality correlation profile can be used to describe the metabolic networks and distinguish them from their random counter-parts with the preserved degree distribution.