L1centGROUP {L1centrality}R Documentation

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)

## S3 method for class 'igraph'
L1centGROUP(
  g,
  nodes,
  eta = NULL,
  mode = c("centrality", "prestige"),
  method = c("minimum", "maximum", "average")
)

## S3 method for class 'matrix'
L1centGROUP(
  g,
  nodes,
  eta = NULL,
  mode = c("centrality", "prestige"),
  method = "minimum"
)

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.

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.

Value

A list consisting of two objects:

Note

The function is valid only for connected graphs. If the graph is directed, it must be strongly connected. Multiple edges (edges with the same head and tail vertices) are not allowed, because they make the edge weight setting procedure confusing.

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)

[Package L1centrality version 0.2.1 Index]