Projects per year
Abstract
We introduce and study a new network centrality measure based on the concept of nonbacktracking walks; that is, walks not containing subsequences of the form uvu where u and v are any distinct connected vertices of the underlying graph. We argue that this feature can yield more meaningful rankings than traditional walk-based centrality measures. We show that the resulting Katz-style centrality measure may be computed via the so-called deformed graph Laplacian—a quadratic matrix polynomial that can be associated with any graph. By proving a range of new results about this matrix polynomial, we gain insights into the behavior of the algorithm with respect to its Katz-like parameter. The results also inform implementation issues. In particular we show that, in an appropriate limit, the new measure coincides with the nonbacktracking version of eigenvector centrality introduced by Martin, Zhang and Newman in 2014. Rigorous analysis on star and star-like networks illustrates the benefits of the new approach, and further results are given on real networks.
Original language | English |
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Pages (from-to) | 310-341 |
Number of pages | 32 |
Journal | SIAM Journal on Matrix Analysis and Applications |
Volume | 39 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Mar 2018 |
Keywords
- centrality index
- deformed graph Laplacian
- matrix polynomial
- nonbacktracking
- complex networks
- generating function
Projects
- 1 Finished
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Data Analytics for Future Cities
Higham, D.
EPSRC (Engineering and Physical Sciences Research Council)
1/01/15 → 31/12/19
Project: Research Fellowship