L1centrality (version 0.4.0)

L1centNB: L1 Centrality/Prestige-Based Neighborhood

Description

Derives L₁ centrality- or L₁ prestige-based neighborhood of each vertex. For undirected graphs, the two neighborhood are identical.

Usage

L1centNB(g, eta, mode, weight_transform)
# S3 method for igraph
L1centNB(
  g,
  eta = NULL,
  mode = c("centrality", "prestige"),
  weight_transform = NULL
)
# S3 method for matrix
L1centNB(
  g,
  eta = NULL,
  mode = c("centrality", "prestige"),
  weight_transform = NULL
)
# S3 method for L1centNB
print(x, ...)
# S3 method for L1centNB
summary(object, ...)

Value

L1centNB() returns an object of class L1centNB. It is a list of numeric vectors. The length of the list is equivalent to the number of vertices in the graph g, and the names of the list are vertex names. Each component of the list is a numeric vector whose length is equivalent to the number of vertices in the graph g. Specifically, the ith component of the list is a vector of the L₁ centrality of each vertex, for the modified graph g

w.r.t. the ith vertex (if mode = "centrality") or the L₁ prestige of each vertex, for the modified graph g

w.r.t. the ith vertex (if mode = "prestige").

print.L1centNB() prints L₁ centrality or L₁ prestige values at the modified graph w.r.t. each vertex and returns them invisibly.

summary.L1centNB() returns an object of class table. It is a summary of the prominence values with the five-number summary, mean, and the Gini coefficient, at each modified graph.

Arguments

g

An igraph graph object or a distance matrix. The graph must be connected. For a directed graph, it must be strongly connected. Equivalently, all entries of the distance matrix must be finite. Here, the (i,j) component of the distance matrix is the geodesic distance from the ith vertex to the jth vertex.

eta

An optional nonnegative multiplicity (weight) vector for (vertex) weighted networks. The sum of its components must be positive. If set to NULL (the default), all vertices will have the same positive weight (multiplicity) of 1, i.e., g is treated as a vertex unweighted graph. The length of the eta must be equivalent to the number of vertices.

mode

A character string. For an undirected graph, either choice gives the same result.

• centrality (the default): L₁ centrality (prominence of each vertex in terms of making a choice) is used for analysis.

• prestige: L₁ prestige (prominence of each vertex in terms of receiving a choice) is used for analysis.

weight_transform

An optional function to transform the edge weights when g is an igraph object and an edge weight attribute exists. This argument is ignored when g is a distance matrix.

x

An L1centNB object, obtained as a result of the function L1cent().

...

Further arguments passed to or from other methods. This argument is ignored here.

object

An L1centNB object, obtained as a result of the function L1centNB().

Details

For an undirected graph, if the graph is symmetrized (in a way defined in Kang and Oh 2025a) w.r.t. a vertex v, vertex v becomes the graph median (Kang and Oh 2025a), i.e., v has L₁ centrality 1. Based on this property, we define the L₁ centrality-based neighborhood of vertex v as vertices that have large L₁ centrality on the symmetrized graph w.r.t. vertex v.

For a directed graph, a vertex of interest, say v, is made to a centrality and prestige median vertex by the procedure described in Kang and Oh (2025b). We call the resulting graph as the modified graph w.r.t. v. L₁ centrality (prestige) -based neighborhood of vertex v is a set of vertices that have large L₁ centrality (prestige) on the modified graph w.r.t. vertex v.

References

S. Kang and H.-S. Oh. On a notion of graph centrality based on L₁ data depth. Journal of the American Statistical Association, 1--13, 2025a.

S. Kang and H.-S. Oh. L₁ prominence measures for directed graphs. The American Statistician, 1--16, 2025b.

See Also

L1cent() for L₁ centrality/prestige, L1centLOC() and L1centEDGE() internally uses L1centNB().

Examples

NB <- L1centNB(MCUmovie, eta = igraph::V(MCUmovie)$worldwidegross)
# Top 6 L1 centrality-based neighbors of "Iron Man"
utils::head(sort(NB$"Iron Man", decreasing = TRUE))