Degree centrality for multilevel networks

Usage

multilevel_degree(
  A1,
  B1,
  A2 = NULL,
  B2 = NULL,
  A3 = NULL,
  B3 = NULL,
  complete = FALSE,
  digraphA1 = FALSE,
  digraphA2 = FALSE,
  digraphA3 = FALSE,
  typeA1 = "out",
  typeA2 = "out",
  typeA3 = "out",
  loopsA1 = FALSE,
  loopsA2 = FALSE,
  loopsA3 = FALSE,
  normalized = FALSE,
  weightedA1 = FALSE,
  weightedA2 = FALSE,
  weightedA3 = FALSE,
  alphaA1 = 0.5,
  alphaA2 = 0.5,
  alphaA3 = 0.5
)

Arguments

A1: The square matrix of the lowest level
B1: The incidence matrix of the ties between the nodes of first level and the nodes of the second level
A2: The square matrix of the second level
B2: The incidence matrix of the ties between the nodes of the second level and the nodes of the third level
A3: The square matrix of the third level
B3: The incidence matrix of the ties between the nodes of the third level and the nodes of the first level
complete: Add the degree of bipartite and tripartite networks for B1, B2 and/or B3, and the low_multilevel (i.e. A1+B1+B2+B3), meso_multilevel (i.e. B1+A2+B2+B3) and high_multilevel (i.e. B1+B2+A3+B3) degree
digraphA1: Whether A1 is a directed network
digraphA2: Whether A2 is a directed network
digraphA3: Whether A3 is a directed network
typeA1: Type of degree of the network for A1, "out" for out-degree, "in" for in-degree or "all" for the sum of the two
typeA2: Type of degree of the network for A2, "out" for out-degree, "in" for in-degree or "all" for the sum of the two
typeA3: Type of degree of the network for A3, "out" for out-degree, "in" for in-degree or "all" for the sum of the two
loopsA1: Whether the loops of the edges are considered in matrix A1
loopsA2: Whether the loops of the edges are considered in matrix A2
loopsA3: Whether the loops of the edges are considered in matrix A3
normalized: If TRUE then the result is divided by (n-1)+k+m for the first level, (m-1)+n+k for the second level, and (k-1)+m+n according to Espinosa-Rada et al. (2021)
weightedA1: Whether A1 is weighted
weightedA2: Whether A2 is weighted
weightedA3: Whether A3 is weighted
alphaA1: The alpha parameter of A1 according to Opsahl et al (2010) for weighted networks. The value 0.5 is given by default.
alphaA2: The alpha parameter of A2 according to Opsahl et al (2010) for weighted networks. The value 0.5 is given by default.
alphaA3: The alpha parameter of A3 according to Opsahl et al (2010) for weighted networks. The value 0.5 is given by default.

Value

Return a data.frame of multilevel degree

References

Borgatti, S. P., and Everett, M. G. (1997). Network analysis of 2-mode data. Social Networks, 19(3), 243–269.

Freeman, L. C. (1978). Centrality in social networks conceptual clarification. Social Networks, 1(3), 215–239.

Opsahl, T., Agneessens, F., and Skvoretz, J. (2010). Node centrality in weighted networks: Generalizing degree and shortest paths. Social Networks, 32(3), 245–251.

Author

Alejandro Espinosa-Rada

Examples


A1 <- matrix(c(
  0, 1, 0, 0, 0,
  1, 0, 0, 1, 0,
  0, 0, 0, 1, 0,
  0, 1, 1, 0, 1,
  0, 0, 0, 1, 0
), byrow = TRUE, ncol = 5)

B1 <- matrix(c(
  1, 0, 0,
  1, 1, 0,
  0, 1, 0,
  0, 1, 0,
  0, 1, 1
), byrow = TRUE, ncol = 3)

A2 <- matrix(c(
  0, 1, 1,
  1, 0, 0,
  1, 0, 0
), byrow = TRUE, nrow = 3)

B2 <- matrix(c(
  1, 1, 0, 0,
  0, 0, 1, 0,
  0, 0, 1, 1
), byrow = TRUE, ncol = 4)

A3 <- matrix(c(
  0, 1, 1, 1,
  1, 0, 0, 0,
  1, 0, 0, 1,
  1, 0, 1, 0
), byrow = TRUE, ncol = 4)

B3 <- matrix(c(
  1, 0, 0, 0, 0,
  0, 1, 0, 1, 0,
  0, 0, 0, 0, 0,
  0, 0, 0, 0, 0
), byrow = TRUE, ncol = 5)

multilevel_degree(A1, B1, A2, B2, A3, B3)
#>    multilevel
#> n1          3
#> n2          5
#> n3          2
#> n4          5
#> n5          3
#> m1          6
#> m2          6
#> m3          4
#> k1          5
#> k2          4
#> k3          4
#> k4          3
if (FALSE) {
multilevel_degree(A1, B1, A2, B2, A3, B3, normalized = TRUE, complete = TRUE)
}