Geodesic distances

Matrix of geodesic distances and a summary of the distances of the network.

Usage

geo_distances(
  A,
  digraph = TRUE,
  type = c("out", "in", "all"),
  weighted = FALSE,
  alpha = 1
)

geo_summary(A, digraph = TRUE, weighted = FALSE, alpha = 1)

Arguments

A

A square matrix

digraph

Whether the matrix is directed or undirected

type

Whether to use the out (default), in or all distances

weighted

Whether the matrix is weighted

alpha

The tuning parameter of Opsahl et al. (2010) to transform weights into lengths

Value

geo_distances returns a matrix of distances, and geo_summary the diameter, the average distance and the proportion of reachable pairs.

Details

geo_distances returns the length of the shortest path between every pair of nodes, computed with the Floyd-Warshall algorithm in matrix form. The distance is infinite when there is no path. For valued matrices, the weights are treated as strengths and transformed into lengths as \(1 / w^{\alpha}\) (Opsahl et al., 2010).

geo_summary returns the diameter (the longest geodesic distance), the average distance and the proportion of ordered pairs that can reach each other. When the network is disconnected, both the diameter and the average distance only consider the pairs that are connected by a path.

References

Opsahl, T., Agneessens, F., and Skvoretz, J. (2010). Node centrality in weighted networks: Generalizing degree and shortest paths. Social Networks, 32(3), 245–251. doi:10.1016/j.socnet.2010.03.006

Wasserman, S. and Faust, K. (1994). Social network analysis: Methods and applications. Cambridge University Press.

Author

Alejandro Espinosa-Rada

Examples

A <- matrix(c(
  0, 1, 1, 0, 0, 0,
  0, 0, 0, 1, 1, 0,
  0, 0, 0, 0, 1, 0,
  0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 1,
  0, 0, 0, 0, 0, 0
), byrow = TRUE, nrow = 6)
rownames(A) <- letters[1:nrow(A)]
colnames(A) <- letters[1:ncol(A)]

geo_distances(A)
#>     a   b   c   d   e   f
#> a   0   1   1   2   2   3
#> b Inf   0 Inf   1   1   2
#> c Inf Inf   0 Inf   1   2
#> d Inf Inf Inf   0 Inf Inf
#> e Inf Inf Inf Inf   0   1
#> f Inf Inf Inf Inf Inf   0
geo_summary(A)
#> $diameter
#> [1] 3
#> 
#> $average_distance
#> [1] 1.545455
#> 
#> $prop_reachable
#> [1] 0.3666667
#>