Sensitivity of Centrality and Centralization Measures to the Level of Decentralization in the Network Structure

Abstract

Analytic expressions for node centrality and network centralization measures based on degree, betweenness, closeness, and eigenvector centrality are derived for network topologies with varying levels of decentralization. A solution to known difficulties related to normalization in computing graph centralization using eigenvector centrality is proposed. The correlations between these centrality measures are analyzed. Findings reveal that these measures are highly sensitive to the degree of decentralization in the network. The analytical expressions of these measures would be useful to get deeper insights into the sensitivity of these measures to the underlying structure and in approximating their values for resembling empirical network.