L1centLOC {L1centrality} | R Documentation |
Local L1 Centrality/Prestige
Description
Computes local L1
centrality or local L1
prestige at each alpha
level for every vertex. For undirected graphs,
the two measures are identical.
Usage
L1centLOC(g, eta, alpha, mode)
## S3 method for class 'igraph'
L1centLOC(g, eta = NULL, alpha, mode = c("centrality", "prestige"))
## S3 method for class 'matrix'
L1centLOC(g, eta = NULL, alpha, mode = c("centrality", "prestige"))
Arguments
g |
An |
eta |
An optional nonnegative multiplicity (weight) vector for (vertex)
weighted networks. The sum of its components must be positive. If set to
|
alpha |
A number or a numeric vector of locality levels. Values must be between 0 and 1. |
mode |
A character string. For an undirected graph, either choice gives the same result.
|
Details
Suppose that the given graph has n
vertices. We choose about n\alpha
vertices
(L1 centrality- or
L1 prestige-based
neighborhood) for each vertex (see L1centNB()
), and compute the
L1 centrality or
L1 prestige of the vertex
conditioned on these vertices, i.e., derive the
L1 centrality or
L1 prestige locally. For
details, refer to Kang and Oh (2024a) for undirected graphs, and Kang and Oh
(2024b) for directed graphs.
Value
A list of numeric vectors. The length of the list is equivalent to
the length of alpha
, and the names of the list are the values of
alpha
. Each component of the list is a numeric vector whose length
is equivalent to the number of vertices in the graph g
.
Specifically, the i
th component of the list is a vector of local
L1 centrality at level
alpha[i]
for each vertex (if mode = "centrality"
) or local
L1 prestige at level
alpha[i]
for each vertex (if mode = "prestige"
).
Note
The function is valid only for connected graphs. If the graph is directed, it must be strongly connected.
References
S. Kang and H.-S. Oh. On a notion of graph centrality based on L1 data depth. arXiv preprint arXiv:2404.13233, 2024a.
S. Kang and H.-S. Oh. L1 prominence measures for directed graphs. arXiv preprint arXiv:2408.12078, 2024b.
See Also
L1cent()
for
L1 centrality/prestige,
L1centNB()
for L1
centrality/prestige-based neighborhood.
Examples
weight <- igraph::V(MCUmovie)$worldwidegross
MCUmovie_cent <- L1cent(MCUmovie, eta = weight)
MCUmovie_loc_cent <- L1centLOC(MCUmovie, eta = weight, alpha = 5/32)
plot(MCUmovie_cent, MCUmovie_loc_cent[[1]],
xlab="Global L1 centrality", ylab="Local L1 centrality (alpha = 5/32)",
main="MCU movie network: global vs. local centrality")
graphics::text(MCUmovie_cent, MCUmovie_loc_cent[[1]], igraph::V(MCUmovie)$name)