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Bonacich normalization

Source: R/similarities.R
bonacich_norm.Rd

The function provide a normalisation provided by Bonacich (1972).

Usage

bonacich_norm(A, projection = c("rows", "columns"), normalisation = FALSE)

Source

Adapted from Borgatti, S., Everett, M., Johnson, J. and Agneessens, P. (2022) Analyzing Social Networks Using R. Sage.

Arguments

A

An incidence matrix

projection

Whether to normalise by rows (default), or columns of the matrix.

normalisation

Normalise the measure

Value

This function returns the Bonacich normalisation.

References

Bonacich, P. (1972). Factoring and weighting approaches to status scores and clique identification. Journal of Mathematical Sociology, 2: 112-120.

Examples

A <- matrix(
  c(
    1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0,
    1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0,
    0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0,
    1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0,
    0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1,
    0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1,
    0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1,
    0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0
  ),
  byrow = TRUE, ncol = 14
)
bonacich_norm(A)
#>            [,1]      [,2]      [,3]      [,4]      [,5]      [,6]      [,7]
#>  [1,] 1.0000000 0.7947869 0.8554094 0.7947869 0.6339746 1.0000000 0.6339746
#>  [2,] 0.7947869 1.0000000 0.7947869 0.8571429 0.6796228 1.0000000 1.0000000
#>  [3,] 0.8554094 0.7947869 1.0000000 0.7947869 1.0000000 1.0000000 1.0000000
#>  [4,] 0.7947869 0.8571429 0.7947869 1.0000000 1.0000000 1.0000000 1.0000000
#>  [5,] 0.6339746 0.6796228 1.0000000 1.0000000 1.0000000 0.6666667 0.6666667
#>  [6,] 1.0000000 1.0000000 1.0000000 1.0000000 0.6666667 1.0000000 0.8386095
#>  [7,] 0.6339746 1.0000000 1.0000000 1.0000000 0.6666667 0.8386095 1.0000000
#>  [8,] 1.0000000 0.6077190 1.0000000 0.6077190 0.0000000 0.7500000 0.7500000
#>  [9,] 0.6339746 0.6796228 1.0000000 0.6796228 0.6666667 0.6666667 0.8386095
#> [10,] 0.4494897 0.5000000 0.6339746 0.5000000 0.4686270 0.4686270 0.6666667
#> [11,] 0.4494897 0.3203772 0.4494897 0.3203772 0.0000000 0.4686270 0.4686270
#> [12,] 0.2898979 0.2052131 0.2898979 0.2052131 0.0000000 0.3660254 0.3660254
#> [13,] 0.2052131 0.2857143 0.3538894 0.2857143 0.3203772 0.3203772 0.5000000
#> [14,] 0.0000000 0.2052131 0.2572843 0.2052131 0.2742919 0.2742919 0.4494897
#> [15,] 0.2108967 0.4220645 0.3660254 0.4220645 0.4142136 0.4142136 0.6043561
#> [16,] 1.0000000 0.5000000 1.0000000 0.5000000 0.0000000 0.6339746 0.6339746
#> [17,] 0.4580399 0.0000000 0.4580399 0.0000000 0.0000000 0.0000000 0.0000000
#> [18,] 0.4580399 0.0000000 0.4580399 0.0000000 0.0000000 0.0000000 0.0000000
#>            [,8]      [,9]     [,10]     [,11]     [,12]     [,13]     [,14]
#>  [1,] 1.0000000 0.6339746 0.4494897 0.4494897 0.2898979 0.2052131 0.0000000
#>  [2,] 0.6077190 0.6796228 0.5000000 0.3203772 0.2052131 0.2857143 0.2052131
#>  [3,] 1.0000000 1.0000000 0.6339746 0.4494897 0.2898979 0.3538894 0.2572843
#>  [4,] 0.6077190 0.6796228 0.5000000 0.3203772 0.2052131 0.2857143 0.2052131
#>  [5,] 0.0000000 0.6666667 0.4686270 0.0000000 0.0000000 0.3203772 0.2742919
#>  [6,] 0.7500000 0.6666667 0.4686270 0.4686270 0.3660254 0.3203772 0.2742919
#>  [7,] 0.7500000 0.8386095 0.6666667 0.4686270 0.3660254 0.5000000 0.4494897
#>  [8,] 1.0000000 0.7500000 0.7500000 0.7500000 0.6516685 0.6077190 0.5635083
#>  [9,] 0.7500000 1.0000000 0.8386095 0.6666667 0.5505103 0.6796228 0.4494897
#> [10,] 0.7500000 0.8386095 1.0000000 0.8386095 0.7257081 1.0000000 0.6339746
#> [11,] 0.7500000 0.6666667 0.8386095 1.0000000 1.0000000 1.0000000 0.6339746
#> [12,] 0.6516685 0.5505103 0.7257081 1.0000000 1.0000000 1.0000000 0.7427157
#> [13,] 0.6077190 0.6796228 1.0000000 1.0000000 1.0000000 1.0000000 0.7947869
#> [14,] 0.5635083 0.4494897 0.6339746 0.6339746 0.7427157 0.7947869 1.0000000
#> [15,] 0.4833148 0.6043561 0.7759908 0.7759908 0.6339746 0.7387961 0.6909830
#> [16,] 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 0.4580399
#> [17,] 0.6909830 0.6339746 0.6339746 0.6339746 0.5419601 0.5000000 1.0000000
#> [18,] 0.6909830 0.6339746 0.6339746 0.6339746 0.5419601 0.5000000 1.0000000
#>           [,15]     [,16]     [,17]     [,18]
#>  [1,] 0.2108967 1.0000000 0.4580399 0.4580399
#>  [2,] 0.4220645 0.5000000 0.0000000 0.0000000
#>  [3,] 0.3660254 1.0000000 0.4580399 0.4580399
#>  [4,] 0.4220645 0.5000000 0.0000000 0.0000000
#>  [5,] 0.4142136 0.0000000 0.0000000 0.0000000
#>  [6,] 0.4142136 0.6339746 0.0000000 0.0000000
#>  [7,] 0.6043561 0.6339746 0.0000000 0.0000000
#>  [8,] 0.4833148 1.0000000 0.6909830 0.6909830
#>  [9,] 0.6043561 1.0000000 0.6339746 0.6339746
#> [10,] 0.7759908 1.0000000 0.6339746 0.6339746
#> [11,] 0.7759908 1.0000000 0.6339746 0.6339746
#> [12,] 0.6339746 1.0000000 0.5419601 0.5419601
#> [13,] 0.7387961 1.0000000 0.5000000 0.5000000
#> [14,] 0.6909830 0.4580399 1.0000000 1.0000000
#> [15,] 1.0000000 0.5857864 0.5857864 0.5857864
#> [16,] 0.5857864 1.0000000 0.7683375 0.7683375
#> [17,] 0.5857864 0.7683375 1.0000000 1.0000000
#> [18,] 0.5857864 0.7683375 1.0000000 1.0000000