Graph level indices
g_summary(x, directed = TRUE)
g_density(x, loops = FALSE)
g_mean_distance(x)
g_correlation(g1, g2, diag = FALSE, weight = TRUE, wf = NULL)
g_reciprocity(x)
g_transitivity(x)
g_diameter(x, directed = is_directed(x), unconnected = TRUE)
g_radius(x, mode = c("all", "out", "in"))
g_compactness(x, mode = c("out", "in", "all"))
g_degree_distribution(
x,
mode = c("out", "in", "all"),
type = c("density", "count"),
cumulative = FALSE,
loops = FALSE,
digits = 3
)graph object
Logical, whether directed or undirected paths are to be
considered. This is ignored for undirected graphs. The default is TRUE
is x is directed and FALSE otherwise
logical, should loops/diagonal be included? Default is FALSE.
This is almost always what you want.
an input graph of class igraph, network, matrix
an input graph of class igraph, network, matrix
logical, indicating whether or not the diagonal should be treated
as valid data. Set this TRUE if and only if the data can contain
loops. Is FALSE by default.
local, should weight be included? Is TRUE by default.
not to be set by the user, for internal use only
Logical, what to do if the graph is unconnected.
If FALSE, the function will return a number that is one larger the
largest possible diameter, which is always the number of vertices.
If TRUE, the diameters of the connected components will be calculated
and the largest one will be returned.
Character constant, gives whether the shortest paths to or from
the given vertices should be calculated for directed graphs.
If out then the shortest paths from the vertex, if in then to
it will be considered. If all, the default, then the corresponding
undirected graph will be used, edge directions will be ignored.
This argument is ignored for undirected graphs.
character, either "density" or "count"
logical, should the raw densities be returned or their cumulative sum
the maximal number of decimals in the result
Calculate several graph level indices.
g_summary(): Summary indices of a graph.
This function provides a few very basic summary indices of a graph. Only the default settings for the underlying functions (from this package) are used. For further investigation, consider those settings.
If directed == TRUE (the default), the graph will be treated as
directed if it is (and as undirected if it is not). When
directed == FALSE a directed graph will be forced to become an undirected
graph using to_symmetric_matrix with rule = "weak".
It can sometimes be informative to compare the summary stats for a directed graph with its undirected equivalent.
g_density(): Density of a graph. Weights are discarded.
Use gden if edge weights are to be used and code is
a graph of class network.
Note that this function computes the density of a bipartite network without
symmetrizing, so the density that is reported is half that of the density
reported by the gden in this specific case.
Also note that edge_density does not correctly deal with
loops, so the current function reports correct density values whereas
edge_density reports incorrect values.
g_mean_distance(): Mean path distance
g_correlation(): Product-moment correlation between two networks.
Missing values are permitted. Takes into account whether the
graph is (un)directed (judged from g1).
NOTE: The input graphs should be of class
igraph,network or
matrix. It is possible to mix graph classes, so correlations can
be calculated between graphs of class network and igraph, for
example.
If a weight attribute is included in the graphs, these are used by default.
It is possible and the most common to provide two graphs directly,
but the function also accepts a list of two graphs or an array
of two graph (so, an array of size 2 x n x n).
In this case, provide the list or array as the g1 argument.
The g2 is ignored if g1 is a list or array.
Internally, the graphs are converted to matrices before correlation is calculated.
g_reciprocity(): Reciprocity
g_transitivity(): Transitivity Transitivity is a triadic, algebraic structural
constraint. In its weak form (which is the common form), the transitive constraint
corresponds to a -> b -> c implying a -> c. This measure returns the fraction
of potentially intransitive triads obeying the weak condition.
In other words, we count the number of triplets in which i -> j,
j -> k, and i -> k, and divide by the number of triplets in which
i -> j and j -> k (regardless of whether there is an i -> k edge).
Weights are discarded. Specific functions that can alternatively be used (and are
called by this function) include gtrans (for objects of
class network) and transitivity (for objects of
class igraph).
The network and igraph implementations differ and can give
somewhat different results.
g_diameter(): Diameter of a graph. Weights are discarded. The diameter is
equal to the maximum eccentricity scores across all vertices.
Substantively, this measures the maximum number of steps that are needed to
connect any two vertices in the graph (given that they are connected).
Use diameter if edge weights are to be used or specific
options are needed.
g_radius(): Radius of a graph. Weights are discarded. The diameter is
equal to the minimum eccentricity scores across all vertices.
Substantively, this measures the minimum number of steps that are needed to
connect any two vertices in the graph (given that they are connected).
In other words, regardless of which vertex is considered, it is not possible
to reach all other vertices from it within fewer than this number of steps.
g_compactness(): Compactness of a graph. Weights are discarded.
The compactness of a graph is the average of the inverse distances across all dyads in the graph. Mathematically:
$$\frac{\sum_{i,j : i \neq j} (\frac{1}{d_{ij}})}{n(n-1)}$$
where the denominator is altered according to the number of dyads in the graph.
If all vertices are directly tied to each other, compactness is 1. The shorter the paths between vertices, the larger the inverse distances become. Hence, the shorter the paths, the higher compactness. As such, it is often seen as a measure of cohesion.
This measure works well for disconnected graphs. Inverse distances between disconnected vertices are 0, so the more disconnected the graph, the lower its compactness.
Thus, the measure runs between 0 (abolutely "uncompact") to 1 (maximally compact).
g_degree_distribution(): Degree distribution.
The distribution of the degrees of the vertices in the graph.
Returns a matrix with the counts or densities for each degree and the degrees themselves as column names. The result can be raw or cumulative (starting from degree 0.
m <- matrix(rbinom(25, 1, 0.5), 5, 5)
diag(m) <- 0
g_density(snafun::to_network(m))
#> [1] 0.5
g_density(snafun::to_igraph(m))
#> [1] 0.5
# when loops matter
g <- igraph::graph( c(1,2, 2,2, 2,3) )
g_density(g, loops = FALSE) # this is wrong, if loops matter
#> [1] 0.5
g_density(g, loops = TRUE) # this is correct, if loops matter
#> [1] 0.3333333
g <- sna::rgraph(10, mode = "digraph")
g_n <- snafun::to_network(g)
g_mean_distance(g_n)
#> [1] 1.411111
g_i <- snafun::to_igraph(g)
g_mean_distance(g_i)
#> [1] 1.411111
g <- sna::rgraph(10, mode = "graph")
g_n <- snafun::to_network(g)
g_mean_distance(g_n)
#> [1] 1.444444
g_i <- snafun::to_igraph(g)
g_mean_distance(g_i)
#> [1] 1.444444
#
# correlation
# matrices
#
g1 <- sna::rgraph(10,1,tprob=c(0.2,0.2,0.5,0.5,0.8,0.8))
g2 <- sna::rgraph(10,1,tprob=c(0.2,0.2,0.5,0.5,0.8,0.8))
g_correlation(g1, g2)
#> [1] 0.09815487
g1 <- to_network(g1); g2 <- to_network(g2)
g_correlation(g1, g2)
#> [1] 0.09815487
g1 <- to_igraph(g1); g2 <- to_igraph(g2)
g_correlation(g1, g2)
#> [1] 0.09815487
#
# reciprocity
g <- igraph::erdos.renyi.game(10, .3, type = "gnp", directed = TRUE)
g_reciprocity(g)
#> [1] 0.4
g_reciprocity(snafun::to_network(g))
#> [1] 0.4
g <- snafun::create_random_graph(10, strategy = "gnm", m = 2, directed = FALSE, graph = "igraph")
g_reciprocity(g)
#> [1] 1
g_reciprocity(snafun::to_network(g))
#> [1] 1
#
# transitivity
data("emon", package = "network")
g <- emon$Cheyenne
is_directed(g) # TRUE
#> [1] TRUE
g_transitivity(g)
#> [1] 0.593361
g_transitivity(to_network(g))
#> [1] 0.593361
data(florentine, package = "snafun")
g <- florentine$flobusiness
is_directed(g) # FALSE
#> [1] FALSE
g_transitivity(g)
#> [1] 0.4166667
g_transitivity(to_network(g))
#> [1] 0.4166667
#
# diameter
g <- igraph::make_ring(10)
g2 <- igraph::delete_edges(g, c(1,2,1,10))
igraph::diameter(g2, unconnected=TRUE)
#> [1] 7
igraph::diameter(g2, unconnected=FALSE)
#> [1] Inf
g_diameter(g2) # 7
#> [1] 7
g_diameter(g2, unconnected = FALSE) # Inf
#> [1] Inf
g_diameter(to_network(g2)) # 7
#> [1] 7
g_diameter(to_network(g2), unconnected = FALSE) # Inf
#> [1] Inf
#
# radius
g_i <- snafun::create_random_graph(10, strategy = "gnp", p = .2,
directed = TRUE, graph = "igraph")
# add isolate
g_i_iso <- igraph::add_vertices(g_i, nv = 1)
igraph::radius(g_i)
#> [1] 2
snafun::v_eccentricity(g_i)
#> [1] 2 2 3 3 3 3 3 2 3 3
snafun::extract_isolates(g_i_iso)
#> [1] 11
snafun::v_eccentricity(g_i_iso) # the isolate has eccentricity 0
#> [1] 2 2 3 3 3 3 3 2 3 3 0
igraph::radius(g_i_iso) # also 0, should raise a flag about isolates
#> [1] 0
g_radius(g_i, mode = "all")
#> [1] 2
g_radius(g_i, mode = "in")
#> [1] 0
g_radius(g_i, mode = "out")
#> [1] 2
g_n <- snafun::to_network(g_i)
g_radius(g_n, mode = "all")
#> [1] 2
g_radius(g_n, mode = "in")
#> [1] 0
g_radius(g_n, mode = "out")
#> [1] 2
#
# compactness
g_i <- snafun::create_random_graph(10, strategy = "gnp", p = .2,
directed = TRUE, graph = "igraph")
# add isolate
g_i_iso <- igraph::add_vertices(g_i, nv = 1)
g_n <- snafun::to_network(g_i)
g_n_iso <- snafun::to_network(g_i_iso)
g_compactness(g_i)
#> [1] 0.4883333
g_compactness(g_n)
#> [1] 0.4883333
g_compactness(g_i, mode = "all") # if direction is irrelevant
#> [1] 0.6666667
g_compactness(g_i_iso)
#> [1] 0.3995455
g_compactness(g_n_iso)
#> [1] 0.3995455
g1 <- igraph::graph_from_literal(A-B-C-D-E-F)
g2 <- igraph::delete_edges(g1, 5)
g3 <- igraph::delete.edges(g1, 3)
#> Warning: `delete.edges()` was deprecated in igraph 2.0.0.
#> ℹ Please use `delete_edges()` instead.
g4 <- igraph::delete_edges(g1, c(4, 5))
g5 <- igraph::delete_edges(g1, c(2, 4))
g_compactness(g1)
#> [1] 0.58
g_compactness(g2)
#> [1] 0.4277778
g_compactness(g3)
#> [1] 0.3333333
g_compactness(g4)
#> [1] 0.2888889
g_compactness(g5)
#> [1] 0.2
#
# degree distribution
g <- snafun::create_random_graph(1000, "gnp", p = .01)
g_degree_distribution(g)
#> 1 2 3 4 5 6 7 8 9 10 11 12 13
#> [1,] 0 0.001 0.005 0.009 0.015 0.041 0.064 0.088 0.118 0.124 0.128 0.108 0.093
#> 14 15 16 17 18 19 20 21
#> [1,] 0.075 0.053 0.036 0.019 0.008 0.005 0.007 0.003