Some New Results on the Eigenvector Centrality

Abstract

In this article we establish new results on the components of the principal eigenvector in an undirected graph. Those results are particularly significant in relation to the concept of centrality in social networks. In particular degree centrality and eigenvector centrality are compared. We find further conditions, based on the spectral radius, on which nodes with highest degree centrality are also the most eigencentral.

Keywords:

• centrality measures
• degree
• eigenvector
• graphs
• social networks
• spectral radius

Notes

¹See Varga (2000), Theorem 2.7 pag. 35.

²Observe that det B _{j, 1} > 0.

³In all the examples nodes are ordered following the degree sequence d ₁ ≥ d ₂ ≥…≥ d _n .