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Abstract
We develop a comprehensive theory for the combinatorics of walkcounting on a directed graph in the case where each backtracking step is downweighted by a given factor. By deriving expressions for the associated generating functions, we also obtain linear systems for computing centrality measures in this setting. In particular, we show that backtrackdownweighted Katzstyle network centrality can be computed at the same cost as standard Katz. Studying the limit of this centrality measure at its radius of convergence also leads to a new expression for backtrackdownweighted eigenvector centrality that generalizes previous work to the case where directed edges are present. The new theory allows us to combine advantages of standard and nonbacktracking cases, avoiding certain types of localization while accounting for treelike structures. We illustrate the behaviour of the backtrackdownweighted centrality measure on both synthetic and real networks.
Original language  English 

Number of pages  19 
Journal  SIAM Journal on Matrix Analysis and Applications 
Publication status  Accepted/In press  6 May 2021 
Keywords
 centrality index
 complex network
 localization
 nonbacktracking walk
 generating function
 zeta function
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 1 Active

Don't look back  nonbacktracking walks in complex networks (ECF)
1/05/19 → 30/04/22
Project: Research Fellowship