Spectral centrality measures in complex networks
Abstract
Complex networks are characterized by heterogeneous distributions of the degree of nodes, which produce a large diversification of the roles of the nodes within the network. Several centrality measures have been introduced to rank nodes based on their topological importance within a graph. Here we review and compare centrality measures based on spectral properties of graph matrices. We shall focus on PageRank (PR), eigenvector centrality (EV), and the hub and authority scores of the HITS algorithm. We derive simple relations between the measures and the (in)degree of the nodes, in some limits. We also compare the rankings obtained with different centrality measures.
 Publication:

Physical Review E
 Pub Date:
 September 2008
 DOI:
 10.1103/PhysRevE.78.036107
 arXiv:
 arXiv:0805.3322
 Bibcode:
 2008PhRvE..78c6107P
 Keywords:

 89.75.Hc;
 Networks and genealogical trees;
 Physics  Physics and Society;
 Condensed Matter  Disordered Systems and Neural Networks;
 Physics  Computational Physics
 EPrint:
 11 pages, 10 figures, 5 tables. Final version published in Physical Review E