Closeness of each node — ntcls • crimlab

Distances are counted in steps (weights are not taken), along edges' directions when dir = TRUE (out-distances). A disconnected graph is handled in the two standard ways, both returned: cls and ncls count only the nodes a node reaches (as igraph::closeness() does), so a node close to the few it reaches scores high; hrm, the harmonic centrality, sums 1 / distance over every other node, an unreachable one adding 0, so reaching more nodes always scores more. Graph rules as in ntdeg().

Usage

ntcls(from, to, nodes = NULL, dir = FALSE)

Arguments

from, to: Labels of the two ends of each edge: vectors of the same length (zero when nodes gives every node) with no missing values.
nodes: NULL, or every node's label once: the node order of the results and the way to include isolated nodes.
dir: TRUE for a directed graph (from sends a tie to to).

Value

A data frame: node, reach (nodes reached), cls (1 / the summed distance to them), ncls (reach / that sum, the inverse mean distance; cls and ncls are NaN when nothing is reached) and hrm (the harmonic centrality).

References

Freeman, L. C. (1978). Centrality in social networks: conceptual clarification. Social Networks, 1(3), 215-239. doi:10.1016/0378-8733(78)90021-7

Marchiori, M. and Latora, V. (2000). Harmony in the small-world. Physica A, 285(3-4), 539-546. doi:10.1016/S0378-4371(00)00311-3

Examples

ntcls(c(1, 2, 3), c(2, 3, 4), nodes = 1:5)
#>   node reach       cls ncls      hrm
#> 1    1     3 0.1666667 0.50 1.833333
#> 2    2     3 0.2500000 0.75 2.500000
#> 3    3     3 0.2500000 0.75 2.500000
#> 4    4     3 0.1666667 0.50 1.833333
#> 5    5     0       NaN  NaN 0.000000