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Abstract
The notions of subgraph centrality and communicability, based on the exponential of the adjacency matrix of the underlying graph, have been effectively used in the analysis of undirected networks. In this paper we propose an extension of these measures to directed networks, and we apply them to the problem of ranking hubs and authorities. The extension is achieved by bipartization, i.e., the directed network is mapped onto a bipartite undirected network with twice as many nodes in order to obtain a network with a symmetric adjacency matrix. We explicitly determine the exponential of this adjacency matrix in terms of the adjacency matrix of the original, directed network, and we give an interpretation of centrality and communicability in this new context, leading to a technique for ranking hubs and authorities. The matrix exponential method for computing hubs and authorities is compared to the well known HITS algorithm, both on small artificial examples and on more realistic realworld networks. A few other ranking algorithms are also discussed and compared with
our technique. The use of Gaussian quadrature rules for calculating hub and authority scores is discussed.
our technique. The use of Gaussian quadrature rules for calculating hub and authority scores is discussed.
Original language  English 

Pages (fromto)  24472474 
Number of pages  28 
Journal  Linear Algebra and its Applications 
Volume  438 
Publication status  Published  2013 
Keywords
 hubs
 authorities
 centrality
 communicability
 matrix exponential
 directed networks
 digraphs
 bipartite graphs
 HITS
 Katz
 PageRank
 Gauss quadrature
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 1 Finished

Mathematics of Large Technological Evolving Networks (MOLTEN)
Higham, D. & Estrada, E.
EPSRC (Engineering and Physical Sciences Research Council)
24/01/11 → 31/03/13
Project: Research