Example undirected graph
# Import libraries
library(scoredec)
library(igraph)
# Create a dummy undirected graph
set.seed(42)
n <- 4
W <- matrix(runif(n^2),n)
W[lower.tri(W)] <- t(W)[lower.tri(W)]
diag(W) <- 0
# Print adjacency matrix
print(W)
## [,1] [,2] [,3] [,4]
## [1,] 0.0000000 0.6417455 0.6569923 0.9346722
## [2,] 0.6417455 0.0000000 0.7050648 0.2554288
## [3,] 0.6569923 0.7050648 0.0000000 0.4622928
## [4,] 0.9346722 0.2554288 0.4622928 0.0000000
# Transform adjacency matrix to graph
g <- graph_from_adjacency_matrix(W, mode = "undirected", weighted = TRUE)
# Set seed for reproducible plot
set.seed(42)
plot(g,
edge.width=E(g)$weight * 5 # make connection weight lines thicker
)
Fig. 2: Example undirected graph with
connectivity lines sized by their weights.
It is clear on Fig. 2 that some
connections are stronger than others, having greater connectivity
weights. Moreover, the same vertex might has some strong and some weak
weights. Therefore, decomposing the graph visually might get hard,
especially on larger networks.
# Get s-core values
s_core_result <- s_coreness(g)
print(s_core_result)
## [1] 3 1 2 3
# Plot result from s_coreness
# Set seed for reproducibility
set.seed(42)
plot(g,
edge.width = E(g)$weight * 5, # make connection weight lines thicker
vertex.size = s_core_result * 10
)
Fig. 3: Example undirected graph with
vertices sized by their s-coreness
It is shown on Fig. 3 that vertices 1 and
4 have higher coreness compared to all the other vertices, while vertex
2 has the smallest one. Note that for undirected graphs the mode
("all","in" or "out") does not
matter:
all.equal(s_core_result, s_coreness(g, mode = "in"))
## [1] TRUE
all.equal(s_core_result, s_coreness(g, mode = "out"))
## [1] TRUE
Therefore, for efficiency reasons, choosing mode = "in"
or mode = "out" is preferred, as long as the sum of
adjacency matrix with its transpose for transforming it to undirected is
not needed.
Example directed graph
# Create a dummy directed graph
set.seed(42)
n <- 4
W <- matrix(runif(n^2),n)
diag(W) <- 0
# Print adjacency matrix
print(W)
## [,1] [,2] [,3] [,4]
## [1,] 0.0000000 0.6417455 0.6569923 0.9346722
## [2,] 0.9370754 0.0000000 0.7050648 0.2554288
## [3,] 0.2861395 0.7365883 0.0000000 0.4622928
## [4,] 0.8304476 0.1346666 0.7191123 0.0000000
# Transform adjacency matrix to graph
g <- graph_from_adjacency_matrix(W, mode = "directed", weighted = TRUE)
# Set seed for reproducible plot
set.seed(42)
plot(g,
edge.width=E(g)$weight * 5, # make connection weight lines thicker,
edge.curved = rep(0.4, ecount(g)) # make directions more visible
)
Fig. 4: Example directed graph with
connectivity lines per direction sized by their weights.
As show on Fig. 4, finding coreness with
both directions and weights is even harder. Therefore, the use of s-core
algorithm is even more cruicial here. In correspondence to the use of
in-degree and out-degree strength of vertices used on k-cores (Csárdi and Nepusz 2006; Csárdi et al. 2024), this algorithm is extended
in the same way as well.
# Get total degree s-core values
all_s_core <- s_coreness(g, mode = "all")
print(all_s_core)
## [1] 3 3 2 1
# Set seed for reproducibility
set.seed(42)
plot(g,
edge.width = E(g)$weight * 5, # make connection weight lines thicker,
edge.curved = rep(0.4, ecount(g)), # make directions more visible
vertex.size = all_s_core * 10
)
Fig. 5: Total degree s-coreness.
# Get in-degree s-core values
in_s_core <- s_coreness(g, mode = "in")
print(in_s_core)
## [1] 2 1 4 3
# Set seed for reproducibility
set.seed(42)
plot(g,
edge.width = E(g)$weight * 5, # make connection weight lines thicker,
edge.curved = rep(0.4, ecount(g)), # make directions more visible
vertex.size = in_s_core * 10
)
Fig. 6: In-degree s-coreness.
# Get out-degree s-core values
out_s_core <- s_coreness(g, mode = "out")
print(out_s_core)
## [1] 3 4 1 2
# Plot result from s_coreness
# Set seed for reproducibility
set.seed(42)
plot(g,
edge.width = E(g)$weight * 5, # make connection weight lines thicker,
edge.curved = rep(0.4, ecount(g)), # make directions more visible
vertex.size = out_s_core * 10
)
Fig. 7: Out-degree s-coreness.
