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Abstract
We develop a comprehensive theory for the combinatorics of walk-counting 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 backtrack-downweighted Katz-style 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 backtrack-downweighted 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 tree-like structures. We illustrate the behaviour of the backtrack-downweighted centrality measure on both synthetic and real networks.
Original language | English |
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Number of pages | 19 |
Journal | SIAM Journal on Matrix Analysis and Applications |
Volume | 42 |
Issue number | 3 |
DOIs | |
Publication status | Published - 30 Sept 2021 |
Keywords
- centrality index
- complex network
- localization
- nonbacktracking walk
- generating function
- zeta function
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Dive into the research topics of 'A theory for backtrack-downweighted walks'. Together they form a unique fingerprint.Projects
- 1 Finished
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Don't look back -- non-backtracking walks in complex networks (ECF)
1/05/19 → 30/04/22
Project: Research Fellowship