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schochastics committed Sep 23, 2024
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10 changes: 5 additions & 5 deletions README.Rmd
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# netrankr <img src="man/figures/logo.png" align="right"/>
[![R-CMD-check](https://github.com/schochastics/netrankr/actions/workflows/R-CMD-check.yaml/badge.svg)](https://github.com/schochastics/netrankr/actions/workflows/R-CMD-check.yaml)
[![CRAN Status Badge](http://www.r-pkg.org/badges/version/netrankr)](https://cran.r-project.org/package=netrankr)
[![CRAN Downloads](http://cranlogs.r-pkg.org/badges/netrankr)](https://CRAN.R-project.org/package=netrankr)
[![CRAN Status Badge](https://www.r-pkg.org/badges/version/netrankr)](https://cran.r-project.org/package=netrankr)
[![CRAN Downloads](https://cranlogs.r-pkg.org/badges/netrankr)](https://CRAN.R-project.org/package=netrankr)
[![Codecov test coverage](https://codecov.io/gh/schochastics/netrankr/branch/main/graph/badge.svg)](https://app.codecov.io/gh/schochastics/netrankr?branch=main)
[![JOSS](https://joss.theoj.org/papers/10.21105/joss.04563/status.svg)](https://doi.org/10.21105/joss.04563)
[![DOI](https://zenodo.org/badge/DOI/10.5281/zenodo.7109041.svg)](https://doi.org/10.5281/zenodo.7109041)
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P
```
[Schoch & Brandes (2016)](https://doi.org/10.1017/S0956792516000401) showed that
$N(u) \subseteq N[v]$ (i.e. `P[u,v]=1`) implies $c(u) \leq c(v)$ for
centrality indices $c$, which are defined via specific path algebras. These include
`P[u,v]=1` implies that u is less central than v for
centrality indices which are defined via specific path algebras. These include
many of the well-known measures like closeness (and variants), betweenness (and variants)
as well as many walk-based indices (eigenvector and subgraph centrality, total communicability,...).

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## Code of Conduct

Please note that the netrankr project is released with a [Contributor Code of Conduct](https://contributor-covenant.org/version/2/1/CODE_OF_CONDUCT.html). By contributing to this project, you agree to abide by its terms.
Please note that the netrankr project is released with a [Contributor Code of Conduct](https://contributor-covenant.org/version/2/1/CODE_OF_CONDUCT.html). By contributing to this project, you agree to abide by its terms.
15 changes: 7 additions & 8 deletions README.md
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[![R-CMD-check](https://github.com/schochastics/netrankr/actions/workflows/R-CMD-check.yaml/badge.svg)](https://github.com/schochastics/netrankr/actions/workflows/R-CMD-check.yaml)
[![CRAN Status
Badge](http://www.r-pkg.org/badges/version/netrankr)](https://cran.r-project.org/package=netrankr)
Badge](https://www.r-pkg.org/badges/version/netrankr)](https://cran.r-project.org/package=netrankr)
[![CRAN
Downloads](http://cranlogs.r-pkg.org/badges/netrankr)](https://CRAN.R-project.org/package=netrankr)
Downloads](https://cranlogs.r-pkg.org/badges/netrankr)](https://CRAN.R-project.org/package=netrankr)
[![Codecov test
coverage](https://codecov.io/gh/schochastics/netrankr/branch/main/graph/badge.svg)](https://app.codecov.io/gh/schochastics/netrankr?branch=main)
[![JOSS](https://joss.theoj.org/papers/10.21105/joss.04563/status.svg)](https://doi.org/10.21105/joss.04563)
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```

[Schoch & Brandes (2016)](https://doi.org/10.1017/S0956792516000401)
showed that $N(u) \subseteq N[v]$ (i.e. `P[u,v]=1`) implies
$c(u) \leq c(v)$ for centrality indices $c$, which are defined via
specific path algebras. These include many of the well-known measures
like closeness (and variants), betweenness (and variants) as well as
many walk-based indices (eigenvector and subgraph centrality, total
communicability,…).
showed that `P[u,v]=1` implies that u is less central than v for
centrality indices which are defined via specific path algebras. These
include many of the well-known measures like closeness (and variants),
betweenness (and variants) as well as many walk-based indices
(eigenvector and subgraph centrality, total communicability,…).

Neighborhood-inclusion defines a partial ranking on the set of nodes.
Each ranking that is in accordance with this partial ranking yields a
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