L1centNB {L1centrality}R Documentation

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)

## S3 method for class 'igraph'
L1centNB(g, eta = NULL, mode = c("centrality", "prestige"))

## S3 method for class 'matrix'
L1centNB(g, eta = NULL, mode = c("centrality", "prestige"))

## S3 method for class 'L1centNB'
print(x, ...)

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.

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.

Details

For an undirected graph, if the graph is symmetrized (in a way defined in Kang and Oh (2024a)) w.r.t. a vertex v, vertex v becomes the graph median (Kang and Oh 2024a), 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 (2024b). 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.

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.

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, L1centLOC() and L1centEDGE() internally uses L1centNB(). Summary for a relevant summary method.

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))

[Package L1centrality version 0.3.1 Index]