L1centEDGE {L1centrality} | R Documentation |
Derives a multiscale edge representation. Each vertex is connected to its local median, which is found in its L1 centrality-based neighborhood.
L1centEDGE(g, eta, alpha)
## S3 method for class 'igraph'
L1centEDGE(g, eta = NULL, alpha)
## S3 method for class 'matrix'
L1centEDGE(g, eta = NULL, alpha)
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. |
In a global perspective, any given undirected graph can be represented as a
star-shaped directed graph, with each vertex making a connection to the
median vertex. Based on this idea, an undirected graph can be represented as
a directed graph, with each vertex making a connection to the local
median vertex. The local median vertex of, say, v_i
, is defined as a
median vertex among the
L1 centrality-based
neighborhood of v_i
. By varying the level of locality, the given graph
can be visually inspected at multiple scales. Refer to Kang and Oh (2024) for
details.
A list of ‘edge lists’. The length of the list is equivalent
to the length of alpha
, and the names of the list are the values of
alpha
. The i
th component of the list is a 2-column matrix,
and each row defines one directed edge, i.e., it is an edge list. The
second column is the local (level alpha[i]
) median of the vertex at
the first column. There may be more than one edge from each vertex, since
there may be more than one local median.
The function is valid only for undirected and connected graphs.
S. Kang and H.-S. Oh. On a notion of graph centrality based on L1 data depth. arXiv preprint arXiv:2404.13233, 2024.
L1cent()
, L1centNB()
, L1centLOC()
. Using the output, one can
use igraph::graph_from_edgelist()
for creating an igraph
object.
See the example code below.
library(igraph)
MCU_edge <- L1centEDGE(MCUmovie, eta = V(MCUmovie)$worldwidegross, alpha = 5/32)
graph <- graph_from_edgelist(MCU_edge[[1]], directed = TRUE)
plot(graph)