View source: R/positional.dominance.R

positional_dominance | R Documentation |

generalized dominance relations that can be computed on one and two mode networks.

```
positional_dominance(A, type = "one-mode", map = FALSE, benefit = TRUE)
```

`A` |
Matrix containing attributes or relations, for instance calculated by indirect_relations. |

`type` |
A string which is either 'one-mode' (Default) if |

`map` |
Logical scalar, whether rows can be sorted or not (Default). See Details. |

`benefit` |
Logical scalar, whether the attributes or relations are benefit or cost variables. |

Positional dominance is a generalization of neighborhood-inclusion for
arbitrary network data. In the default case, it checks for all pairs `u,v`

if
`A_{ut} \ge A_{vt}`

holds for all `t`

if `benefit = TRUE`

or
`A_{ut} \le A_{vt}`

holds for all `t`

if `benefit = FALSE`

.
This form of dominance is referred to as *dominance under total heterogeneity*.
If `map=TRUE`

, the rows of `A`

are sorted decreasingly (`benefit = TRUE`

)
or increasingly (`benefit = FALSE`

) and then the dominance condition is checked. This second
form of dominance is referred to as *dominance under total homogeneity*, while the
first is called *dominance under total heterogeneity*.

Dominance relations as matrix object. An entry `[u,v]`

is `1`

if u is dominated by v.

David Schoch

Brandes, U., 2016. Network positions. *Methodological Innovations* 9,
2059799116630650.

Schoch, D. and Brandes, U., 2016. Re-conceptualizing centrality in social networks.
*European Journal of Applied Mathematics* 27(6), 971-985.

neighborhood_inclusion, indirect_relations, exact_rank_prob

```
library(igraph)
data("dbces11")
P <- neighborhood_inclusion(dbces11)
comparable_pairs(P)
# positional dominance under total heterogeneity
dist <- indirect_relations(dbces11, type = "dist_sp")
D <- positional_dominance(dist, map = FALSE, benefit = FALSE)
comparable_pairs(D)
# positional dominance under total homogeneity
D_map <- positional_dominance(dist, map = TRUE, benefit = FALSE)
comparable_pairs(D_map)
```

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.