Eigenvector centralization as a measure of structural bias in information aggregation

Abstract

The principal eigenvector of the adjacency matrix is widely used to complement degree, betweenness and closeness measures of network centrality. Employing eigenvector centrality as an individual level metric underutilizes this measure. Here we demonstrate how eigenvector centralization, used as a network-level metric, models the potential, or limitation, for the diffusion of novel information within a network. We relate eigenvector centralization to assortativity and core – periphery and use simple simulations to demonstrate how eigenvector centralization is ideal for revealing the conditions under which network structure produces suboptimal utilization of available information. Our findings provide a structural explanation for the persistence of “out of touch” business and political leadership even when organizations implement protocols and interventions to improve leadership accessibility.

KEYWORDS:

• Eigenvector Centrality
• Centralization
• Assortativity
• Social Networks

Notes

¹ Groupthink research has operationalized cohesiveness as mutual attraction (Leana, 1985) and social identity maintenance (Turner & Prakanis, 1998) with limited success. We propose a structural explanation in place of the conventional social psychological explanation.

² Note that this amalgamation issue in networks is different from the classic much studied problem of how information becomes more and more distorted as it passes through a network.

³ Jia et al. (2015) also explore the conditions for equality in decision-making but they use the particular parameters of the Friedkin-Johnsen model to vary the degree of democratic decision-making, not the exclusiveness of the core.

⁴ We also looked at networks with a power law distribution of degree generated by preferential attachment. The results were essentially the same. Although the power law networks have a stronger core-periphery pattern, we decided to use Erdös-Rényi random graphs because their properties are better known.

⁵ Mathematica version 11 was used to generate simulated networks.

⁶ The relationship between centralization and assortativity may be different for different measures of centrality: betweenness, closeness, etc. Kang (2007) has found a negative relationship between centralization and assortativity but his analysis is based entirely on degree centrality, not eigenvector centrality. In eigenvector centrality centralization increases as central members connect to one another.