L1centrality (version 0.4.0)

L1centGROUP: Group L1 Centrality/Prestige

Description

Computes group L₁ centrality or group L₁ prestige for the specified group of vertices. For undirected graphs, the two measures are identical.

Usage

L1centGROUP(g, nodes, eta, mode, method, weight_transform)
# S3 method for igraph
L1centGROUP(
  g,
  nodes,
  eta = NULL,
  mode = c("centrality", "prestige"),
  method = c("minimum", "maximum", "average"),
  weight_transform = NULL
)
# S3 method for matrix
L1centGROUP(
  g,
  nodes,
  eta = NULL,
  mode = c("centrality", "prestige"),
  method = "minimum",
  weight_transform = NULL
)
# S3 method for L1centGROUP
print(x, ...)

Value

L1centGROUP() returns an object of class L1centGROUP. It is a numeric value of the group L₁ centrality (if mode = "centrality") or the group L₁ prestige (if mode = "prestige") of the specified group of vertices.

print.L1centGROUP() prints group L₁ centrality or group L₁ prestige value and returns it invisibly.

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.

nodes

A vector of integers. Each integer indicates the index of the 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.

method

A character string. It specifies the method of setting the edge weight between the pseudo-vertex and the other vertices. Note that the S3 method for the matrix class only supports the minimum option. This is because it is not possible to derive the group reduced graph's distance matrix from the original distance matrix when using the maximum or average method. On the other hand, the group reduced graph's distance matrix can be derived from the original distance matrix when the minimum method is used. See the discussion in Kang (2025).

• minimum (the default): the minimum method is used in setting the edge weights.

• maximum: the maximum method is used in setting the edge weights.

• average: the average method is used in setting the edge weights.

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 L1centGROUP object, obtained as a result of the function L1centGROUP().

...

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

Details

Given a group of vertices on a graph, we first construct a group reduced graph by replacing the group of vertices by a single ‘pseudo-vertex’ (see group_reduce() for the method of setting vertex multiplicities and edge weights in the group reduced graph). The group L₁ centrality (prestige) of this group is defined as the L₁ centrality (prestige) of the pseudo-vertex in the group reduced graph.

References

S. Kang. Topics in Non-Euclidean Dimension Reduction. PhD thesis, Seoul National University, 2025.

See Also

L1cent() for L₁ centrality/prestige, group_reduce() for details on the minimum, maximum, and average methods.

Examples

# Group L1 centrality of the 'Spider-Man' series
vertex_weight <- igraph::V(MCUmovie)$worldwidegross
L1centGROUP(MCUmovie, nodes = c(16,23,27), eta = vertex_weight)