Package 'clustAnalytics'

Average Degree

Description

Average degree (weighted degree, if the graph is weighted) of a graph's communities.

Usage

average_degree(g, com)

Arguments

g	Graph to be analyzed (as an igraph object). If the edges have a "weight" attribute, those will be used as weights.
com	community membership integer vector. Each element corresponds to a vertex.

Value

Numeric vector with the average degree of each community.

See Also

Other cluster scoring functions: FOMD(), average_odf(), conductance(), coverage(), cut_ratio(), density_ratio(), edges_inside(), expansion(), internal_density(), max_odf(), normalized_cut(), scoring_functions(), weighted_clustering_coefficient(), weighted_transitivity()

Examples

data(karate, package="igraphdata")
average_degree(karate, membership(cluster_louvain(karate)))

---

Average Out Degree Fraction

Description

Computes the Average Out Degree Fraction (Average ODF) of a graph (which can be weighted) and its communities.

Usage

average_odf(g, com)

Arguments

g	Graph to be analyzed (as an igraph object). If the edges have a "weight" attribute, those will be used as weights (otherwise, all edges are assumed to be 1).
com	Community membership integer vector. Each element corresponds to a vertex of the graph, and contains the index of the community it belongs to.

Value

Numeric vector with the Average ODF of each community.

See Also

Other cluster scoring functions: FOMD(), average_degree(), conductance(), coverage(), cut_ratio(), density_ratio(), edges_inside(), expansion(), internal_density(), max_odf(), normalized_cut(), scoring_functions(), weighted_clustering_coefficient(), weighted_transitivity()

Examples

data(karate, package="igraphdata")
average_odf(karate, membership(cluster_louvain(karate)))

---

Generates a Barabási-Albert graph with community structure

Description

Generates a Barabási-Albert graph with community structure

Usage

barabasi_albert_blocks(
  m,
  p,
  B,
  t_max,
  G0 = NULL,
  t0 = NULL,
  G0_labels = NULL,
  sample_with_replacement = FALSE,
  type = "Hajek"
)

Arguments

m	number of edges added at each step.
p	vector of label probabilities. If they don't sum 1, they will be scaled accordingly.
B	matrix indicating the affinity of vertices of each label.
t_max	maximum value of t (which corresponds to graph order)
G0	initial graph
t0	t value at which new vertex start to be attached. If G0 is provided, this argument is ignored and assumed to be gorder(G0)+1. If it isn't, a G0 graph will be generated with order t0-1.
G0_labels	labels of the initial graph. If NULL, they will all be set to 1.
sample_with_replacement	If TRUE, allows parallel edges.
type	Either "Hajek" or "block_first".

Value

The resulting graph, as an igraph object. The vertices have a "label" attribute.

Examples

B <- matrix(c(1, 0.2, 0.2, 1), ncol=2)
G <- barabasi_albert_blocks(m=4, p=c(0.5, 0.5), B=B, t_max=100, type="Hajek", 
                            sample_with_replacement = FALSE)

---

Performs nonparametric bootstrap to a graph and a list of clustering algorithms

Description

Performs nonparametric bootstrap on a graph's by resampling its vertices and clustering the results using a list of clustering algorithms.

Usage

boot_alg_list(
  alg_list = list(Louvain = cluster_louvain, `label prop` = cluster_label_prop, walktrap
    = cluster_walktrap),
  g,
  R = 999,
  return_data = FALSE,
  type = "global"
)

Arguments

alg_list	List of igraph clustering algorithms
g	igraph graph object
R	Number of bootstrap replicates.
return_data	Logical. If TRUE, returns a list of "boot" objects with the full results. Otherwise, returns a table with the mean results.
type	Can be "global" (Variation of Information, Reduced Mutual Information, and adjusted Rand Index) or "cluster-wise" (Jaccard distance)

Value

If return_data is set to TRUE, returns a list of objects of class "boot" (see boot). Otherwise, returns as table with the mean distances from the clusters in the original graph to the resampled ones, for each of the algorithms.

---

Conductance

Description

Conductance of a graph's communities, which is given by

$\frac{c_s}{2m_s + c_s}$

, where $c_s$ is the weight of the edges connecting the community s to the rest of the graph, and m_s is the internal weight of the community.

Usage

conductance(g, com)

Arguments

g	Graph to be analyzed (as an igraph object). If the edges have a "weight" attribute, those will be used as weights.
com	community membership integer vector. Each element corresponds to a vertex.

Value

Numeric vector with the conductance of each community.

See Also

Other cluster scoring functions: FOMD(), average_degree(), average_odf(), coverage(), cut_ratio(), density_ratio(), edges_inside(), expansion(), internal_density(), max_odf(), normalized_cut(), scoring_functions(), weighted_clustering_coefficient(), weighted_transitivity()

Examples

data(karate, package="igraphdata")
conductance(karate, membership(cluster_louvain(karate)))

---

Computes possible membership vectors from contingency table

Description

Given a contingency table, obtains a possible pair of corresponding labelings. That is, element M[i,j] is the number of elements that belong to community i in the first labeling and j in the second.

Usage

contingency_to_membership_vectors(M)

Arguments

M	the contingency table

Value

a list containing the two membership vectors

---

Natural logarithm of the number of contingency tables

Description

Given a contingency table, returns the natural logarithm of the number of contingency tables that share the same column and row sums. This implementation combines a Markov Chain Monte Carlo approximation with an analytical formula. The input can be either M a contingency table, or two vectors of labels c1 and c2 (in this case, we are counting contingency tables with the same column an row sums as the one produced by c1 and c2)

Usage

count_contingency_tables_log(c1, c2, M = NULL, monte_carlo_only = FALSE)

Arguments

c1, c2	membership vectors
M	contingency table
monte_carlo_only	Uses only the Monte Carlo approximation

---

Coverage

Description

Computes the coverage (fraction of internal edges with respect to the total number of edges) of a graph and its communities

Usage

coverage(g, com)

Arguments

g	Graph to be analyzed (as an igraph object).
com	Community membership integer vector. Each element corresponds to a vertex of the graph, and contains the index of the community it belongs to.

Value

Numeric value of the coverage of g and com.

See Also

Other cluster scoring functions: FOMD(), average_degree(), average_odf(), conductance(), cut_ratio(), density_ratio(), edges_inside(), expansion(), internal_density(), max_odf(), normalized_cut(), scoring_functions(), weighted_clustering_coefficient(), weighted_transitivity()

Examples

data(karate, package="igraphdata")
coverage(karate, membership(cluster_louvain(karate)))

---

Cut Ratio

Description

The cut ratio of a graph's community is the total edge weight connecting the community to the rest of the graph divided by number of unordered pairs of vertices such that one belongs to the community and the other does not.

Usage

cut_ratio(g, com)

Arguments

g	Graph to be analyzed (as an igraph object). If the edges have a "weight" attribute, those will be used as weights.
com	community membership integer vector. Each element corresponds to a vertex.

Value

Numeric vector with the cut ratio of each community.

See Also

Other cluster scoring functions: FOMD(), average_degree(), average_odf(), conductance(), coverage(), density_ratio(), edges_inside(), expansion(), internal_density(), max_odf(), normalized_cut(), scoring_functions(), weighted_clustering_coefficient(), weighted_transitivity()

Examples

data(karate, package="igraphdata")
cut_ratio(karate, membership(cluster_louvain(karate)))

---

Density Ratio

Description

Density ratio of a graph's communities.

Usage

density_ratio(g, com, type = "local")

Arguments

g	Graph to be analyzed (as an igraph object). If the edges have a "weight" attribute, those will be used as weights.
com	community membership integer vector. Each element corresponds to a vertex.
type	can either be "local" or "global"

Value

Numeric vector with the internal density of each community.

See Also

Other cluster scoring functions: FOMD(), average_degree(), average_odf(), conductance(), coverage(), cut_ratio(), edges_inside(), expansion(), internal_density(), max_odf(), normalized_cut(), scoring_functions(), weighted_clustering_coefficient(), weighted_transitivity()

Examples

data(karate, package="igraphdata")
density_ratio(karate, membership(cluster_louvain(karate)))

---

Edges Inside

Description

Number of edges inside a graph's communities, or their accumulated weight if the graph's edges are weighted.

Usage

edges_inside(g, com)

Arguments

g	Graph to be analyzed (as an igraph object). If the edges have a "weight" attribute, those will be used as weights.
com	community membership integer vector. Each element corresponds to a vertex.

Value

Numeric vector with the internal edge weight of each community

See Also

Other cluster scoring functions: FOMD(), average_degree(), average_odf(), conductance(), coverage(), cut_ratio(), density_ratio(), expansion(), internal_density(), max_odf(), normalized_cut(), scoring_functions(), weighted_clustering_coefficient(), weighted_transitivity()

Examples

data(karate, package="igraphdata")
edges_inside(karate, membership(cluster_louvain(karate)))

---

Estimates |H_0|/|H_r*|

Description

This is the total number of contingency tables (of the same margins as M) divided by the number that match M until the r-th row (included, 0-indexed). Note that if r==0, this is always 1 by definition.

Usage

estimate_H_fraction_r_rows(M, r, error = 0.1)

Arguments

M	contingency table
r	row index
error	error for the convergence of the method

---

Evaluates significance of cluster algorithm results on a graph

Description

Given a graph and a list of clustering algorithms, computes several scoring functions on the clusters found by each of the algorithms.

Usage

evaluate_significance(
  g,
  alg_list = list(Louvain = cluster_louvain, `label prop` = cluster_label_prop, walktrap
    = cluster_walktrap),
  no_clustering_coef = FALSE,
  gt_clustering = NULL,
  w_max = NULL
)

Arguments

g	Graph to be analyzed (as an igraph object)
alg_list	List of clustering algorithms, which take an igraph graph as input and return an object of the communities class.
no_clustering_coef	Logical. If TRUE, skips the computation of the clustering coefficient, which is the most computationally costly of the scoring functions.
gt_clustering	Vector of integers that correspond to labels of the ground truth clustering. The scoring functions will be evaluated on it.
w_max	Numeric. Upper bound for edge weights. Should be generally left as default (NULL).

Value

A data frame with the values of scoring functions (see scoring_functions) of the clusters obtained by applying the clustering algorithms to the graph.

Examples

data(karate, package="igraphdata")
evaluate_significance(karate)

---

Evaluates the significance of a graph's clusters

Description

Computes community scoring functions to the communities obtained by applying the given clustering algorithms to a graph. These are compared to the same scores for randomized versions of the graph obtained by a switching algorithm that rewires edges.

Usage

evaluate_significance_r(
  g,
  alg_list = list(Louvain = cluster_louvain, `label prop` = cluster_label_prop, walktrap
    = cluster_walktrap),
  no_clustering_coef = FALSE,
  gt_clustering = NULL,
  table_style = "default",
  ignore_degenerate_cl = TRUE,
  Q = 100,
  lower_bound = 0,
  weight_sel = "const_var",
  n_reps = 5,
  w_max = NULL
)

Arguments

g	Graph to be analyzed (as an igraph object)
alg_list	List of clustering algorithms, which take an igraph graph as input and return an object of the communities class.
no_clustering_coef	Logical. If TRUE, skips the computation of the clustering coefficient, which is the most computationally costly of the scoring functions.
gt_clustering	Vector of integers that correspond to labels of the ground truth clustering. The scoring functions will be evaluated on it.
table_style	By default returns a table with three columns per algorithm: the original one, the mean of the corresponding rewired scores (suffix "_r") and it's percentile rank within the distribution of rewired scores (suffix "_percentile"). If table_style == "string", instead returns a table with a column per algorithm where each element is of the form "original|rewired(percentile)"
ignore_degenerate_cl	Logical. If TRUE, when computing the means of the scoring functions, samples with only one cluster will be ignored. See rewireCpp.
Q	Numeric. Parameter that controls the number of iterations of the switching algorithm, which will be Q times the order of the graph.
lower_bound	Numeric. Lower bound to the edge weights. The randomization process will avoid steps that would make edge weights fall outside this bound. It should generally be left as 0 to avoid negative weights.
weight_sel	Can be either const_var or max_weight.
n_reps	Number of samples of the rewired graph.
w_max	Numeric. Upper bound for edge weights. The randomization algorithm will avoid steps that would make edge weights fall outside this bound. Should be generally left as default (NULL), unless the network has by nature or by construction a known upper bound.

Value

A matrix with the results of each scoring function and algorithm. See table_style for details.

---

Expansion

Description

Given a graph (possibly weighted) split into communities, the expansion of a community is the sum of all edge weights connecting it to the rest of the graph divided by the number of vertices in the community

Usage

expansion(g, com)

Arguments

g	Graph to be analyzed (as an igraph object). If the edges have a "weight" attribute, those will be used as weights.
com	community membership integer vector. Each element corresponds to a vertex.

Value

Numeric vector with the expansion of each community.

See Also

Other cluster scoring functions: FOMD(), average_degree(), average_odf(), conductance(), coverage(), cut_ratio(), density_ratio(), edges_inside(), internal_density(), max_odf(), normalized_cut(), scoring_functions(), weighted_clustering_coefficient(), weighted_transitivity()

Examples

data(karate, package="igraphdata")
expansion(karate, membership(cluster_louvain(karate)))

---

FOMD (Fraction Over Median Degree)

Description

Given a weighted graph and a partition into communities, returns the fraction of nodes of each community whose internal degree (i.e. the degree accounting only intra-community edges) is greater than the median degree of the whole graph.

Usage

FOMD(g, com, edgelist = NULL)

Arguments

g	Graph to be analyzed (as an igraph object). If the edges have a "weight" attribute, those will be used as weights.
com	Community membership integer vector. Each element corresponds to a vertex.
edgelist	alternatively, the edgelist of the graph, as a matrix where the first two columns to the vertices and the third is the weight of each edge.

Value

Numeric vector with the FOMD of each community.

See Also

Other cluster scoring functions: average_degree(), average_odf(), conductance(), coverage(), cut_ratio(), density_ratio(), edges_inside(), expansion(), internal_density(), max_odf(), normalized_cut(), scoring_functions(), weighted_clustering_coefficient(), weighted_transitivity()

Examples

data(karate, package="igraphdata")
FOMD(karate, membership(cluster_louvain(karate)))

---

Forex correlation network

Description

Network built from correlations between time series of exchange rate returns. It was built from the 13 most traded currencies and with data of January 2009. It is a complete graph of 78 vertices (corresponding to pairs of currencies) and has edge weights bounded between 0 and 1.

Usage

g_forex

Format

An igraph object with 78 vertices and 3003 weighted edges

---

Returns edgelist with weights from a weighted igraph graph

Description

This function is just used internally for testing the package

Usage

igraph_to_edgelist(g, sort = TRUE)

Arguments

g	igraph graph with weighted edges
sort	sorts the edge list lexicographically before returning

Value

A matrix where the first two columns indicate the incident vertices, and the third is the weight of the corresponding edge.

---

Internal Density

Description

Internal density of a graph's communities. That is, the sum of weights of their edges divided by the number of unordered pairs of vertices (which is the number of potential edges).

Usage

internal_density(g, com)

Arguments

g	Graph to be analyzed (as an igraph object). If the edges have a "weight" attribute, those will be used as weights.
com	community membership integer vector. Each element corresponds to a vertex.

Value

Numeric vector with the internal density of each community.

See Also

Other cluster scoring functions: FOMD(), average_degree(), average_odf(), conductance(), coverage(), cut_ratio(), density_ratio(), edges_inside(), expansion(), max_odf(), normalized_cut(), scoring_functions(), weighted_clustering_coefficient(), weighted_transitivity()

Examples

data(karate, package="igraphdata")
internal_density(karate, membership(cluster_louvain(karate)))

---

Make graph weighted

Description

Given a graph, create a "weight" attribute set to 1 for the edges if it doesn't exist already.

Usage

make_graph_weighted(g)

Arguments

g	igraph graph

Value

igraph graph with either all edge weights set to 1 (if the original graph was unweighted), or to their original weights if they already existed (in this case, the graph isn't modified at all).

---

Max Out Degree Fraction

Description

Computes the Maximum Out Degree Fraction (Max ODF) of a graph (which can be weighted) and its communities.

Computes the Flake Out Degree Fraction (Max ODF) of a graph (which can be weighted) and its communities.

Usage

max_odf(g, com)

max_odf(g, com)

Arguments

g	Graph to be analyzed (as an igraph object). If the edges have a "weight" attribute, those will be used as weights (otherwise, all edges are assumed to be 1).
com	Community membership integer vector. Each element corresponds to a vertex of the graph, and contains the index of the community it belongs to.

Value

Numeric vector with the Max ODF of each community.

Numeric vector with the Max ODF of each community.

See Also

Other cluster scoring functions: FOMD(), average_degree(), average_odf(), conductance(), coverage(), cut_ratio(), density_ratio(), edges_inside(), expansion(), internal_density(), normalized_cut(), scoring_functions(), weighted_clustering_coefficient(), weighted_transitivity()

Other cluster scoring functions: FOMD(), average_degree(), average_odf(), conductance(), coverage(), cut_ratio(), density_ratio(), edges_inside(), expansion(), internal_density(), normalized_cut(), scoring_functions(), weighted_clustering_coefficient(), weighted_transitivity()

Examples

data(karate, package="igraphdata")
max_odf(karate, membership(cluster_louvain(karate)))
data(karate, package="igraphdata")
max_odf(karate, membership(cluster_louvain(karate)))

---

Normalized cut

Description

Normalized cut of a graph's communities, which is given by

$\frac{c_s}{2m_s+c_s}+\frac{c_s}{2(m-m_s)+c_s}$

, where $c_s$ is the weight of the edges connecting the community s to the rest of the graph, $m_s$ is the internal weight of the community, and $m$ is the total weight of the network.

Usage

normalized_cut(g, com)

Arguments

g	Graph to be analyzed (as an igraph object). If the edges have a "weight" attribute, those will be used as weights.
com	community membership integer vector. Each element corresponds to a vertex.

Value

Numeric vector with the normalized cut of each community.

See Also

Other cluster scoring functions: FOMD(), average_degree(), average_odf(), conductance(), coverage(), cut_ratio(), density_ratio(), edges_inside(), expansion(), internal_density(), max_odf(), scoring_functions(), weighted_clustering_coefficient(), weighted_transitivity()

Examples

data(karate, package="igraphdata")
normalized_cut(karate, membership(cluster_louvain(karate)))

---

Maximum, Average, and Flake Out Degree Fractions of a Graph Partition

Description

Given a weighted graph and a partition into communities, returns the maximum, average and flake out degree fractions of each community.

Usage

out_degree_fractions(g, com, edgelist)

Arguments

g	Graph to be analyzed (as an igraph object)
com	Community membership vector. Each element corresponds to a vertex of the graph, and contains the index of the community it belongs to.
edgelist	alternatively, the edgelist of the graph

Value

A numeric matrix where each row corresponds to a community, and the columns contain the max, average and flake ODFs respectively.

---

Reduced Mutual Information

Description

Computes the Newman's Reduced Mutual Information (RMI) as defined in (Newman et al. 2020).

Usage

reduced_mutual_information(
  c1,
  c2,
  base = 2,
  normalized = FALSE,
  method = "approximation2",
  warning = TRUE
)

Arguments

c1, c2	membership vectors
base	base of the logarithms used in the calculations. Changing it only scales the final value. By default set to e=exp(1).
normalized	If true, computes the normalized version of the corrected mutual information.
method	Can be "hybrid" (default, combines Monte Carlo with analytical formula), "monte_carlo", approximation1" (appropriate for partitions into many very small clusters), or "approximation2" (for partitions into few larger clusters).
warning	set to false to ignore the warning.

Details

The implementation is based on equations 23 (25 for the normalized case) and 29 in (Newman et al. 2020). The evaluations of the $\Gamma$ functions can get too large and cause overflow issues in the intermediate steps, so the following term of equation 29:

$\frac{1}{2} \log \frac{\Gamma(\mu R) \Gamma(\nu S)} {(\Gamma(\nu)\Gamma(R))^S (\Gamma(\mu)\Gamma(S))^R }$

is rewritten as

$\frac{1}{2} (\log\Gamma(\mu R) + \log\Gamma(\nu S) - S\log(\Gamma(\nu) - S\log(\Gamma(R) - R\log\Gamma(\mu) - R\log\Gamma(R) )$

, and then the function lgamma is used instead of gamma.

Value

The value of Newman's RMI (a scalar).

References

Newman MEJ, Cantwell GT, Young J (2020). “Improved mutual information measure for clustering, classification, and community detection.” Phys. Rev. E, 101(4), 042304. doi:10.1103/PhysRevE.101.042304.

---

Relabels membership vector

Description

Takes a vector of vertex ids indicating community membership, and relabels the communities to have consecutive values from 1 to the number of communities.

Usage

relabel(c)

Arguments

c	numeric vector of vertex ids, not necessarily consecutive

Value

A numeric vector of consecutive vertex ids starting from one

---

Randomizes a weighted graph while keeping the degree distribution constant.

Description

Converts the graph to a weighted edge list in NumericMatrix, which is compatible with Rcpp. The Rcpp function "randomize" is called, and then the resulting edge list is converted back into an igraph object.

Usage

rewireCpp(
  g,
  Q = 100,
  weight_sel = "max_weight",
  lower_bound = 0,
  upper_bound = NULL
)

Arguments

g	igraph graph, which can be weighted.
Q	Numeric. Parameter that controls the number of iterations, which will be Q times the order of the graph.
weight_sel	can be either "const_var" or "max_weight".
lower_bound, upper_bound	Bounds to the edge weights. The randomization process will avoid steps that would make edge weights fall outside these bounds. Set to NULL for no bound. By default, 0 and NULL respectively.

Value

The rewired graph.

---

Scoring Functions of a Graph Partition

Description

Computes the scoring functions of a graph and its clusters.

Usage

scoring_functions(
  g,
  com,
  no_clustering_coef = TRUE,
  type = "local",
  weighted = TRUE,
  w_max = NULL
)

Arguments

g	Graph to be analyzed (as an igraph object). If the edges have a "weight" attribute, those will be used as weights (otherwise, all edges are assumed to be 1).
com	Community membership integer vector. Each element corresponds to a vertex of the graph, and contains the index of the community it belongs to.
no_clustering_coef	Logical. If TRUE, skips the computation of the clustering coefficient (which can be slow on large graphs).
type	can be "local" for a cluster by cluster analysis, or "global" for a global analysis of the whole graph partition.
weighted	Is the graph weighted? If it is, doesn't compute TPR score.
w_max	Numeric. Upper bound for edge weights. Should be generally left as default (NULL). Only affects the computation of the clustering coefficient.

Value

If type=="local", returns a dataframe with a row for each community, and a column for each score. If type=="global", returns a single row with the weighted average scores.

See Also

Other cluster scoring functions: FOMD(), average_degree(), average_odf(), conductance(), coverage(), cut_ratio(), density_ratio(), edges_inside(), expansion(), internal_density(), max_odf(), normalized_cut(), weighted_clustering_coefficient(), weighted_transitivity()

Examples

data(karate, package="igraphdata")
scoring_functions(karate, membership(cluster_louvain(karate)))

---

Sort matrix

Description

Given a matrix, rearranges rows and columns so that row sums and col sums end up in ascending order.

Usage

sort_matrix(M)

Arguments

M

matrix

Value

rearranged matrix

---

Triangle Participation Ratio (community-wise)

Description

Computes the triangle participation ratio (proportion of vertices that belong to a triangle). The computation is done to the subgraphs induced by each of the communities in the given partition.

Usage

triangle_participation_ratio_communities(g, com)

Arguments

g	The input graph (as an igraph object). Edge weights and directions are ignored.
com	Community membership vector. Each element corresponds to a vertex of the graph, and contains the index of the community it belongs to.

Value

A vector containing the triangle participation ratio of each community.

---

Weighted clustering coefficient of a weighted graph.

Description

Weighted clustering Computed using the definition given by McAssey, M. P. and Bijma, F. in "A clustering coefficient for complete weighted networks" (2015).

Usage

weighted_clustering_coefficient(g, upper_bound = NULL)

Arguments

g	igraph graph
upper_bound	upper bound to the edge weights used to compute the integral

Value

The weighted clustering coefficient of the graph (a scalar).

See Also

Other cluster scoring functions: FOMD(), average_degree(), average_odf(), conductance(), coverage(), cut_ratio(), density_ratio(), edges_inside(), expansion(), internal_density(), max_odf(), normalized_cut(), scoring_functions(), weighted_transitivity()

Examples

data(karate, package="igraphdata")
weighted_clustering_coefficient(karate)

---

Weighed transitivity of a weighted graph.

Description

Computed using the definition given by McAssey, M. P. and Bijma, F. in "A clustering coefficient for complete weighted networks" (2015).

Usage

weighted_transitivity(g, upper_bound = NULL)

Arguments

g	igraph graph
upper_bound	upper bound to the edge weights used to compute the integral

Value

The weighted transitivity of the graph (a scalar).

See Also

Other cluster scoring functions: FOMD(), average_degree(), average_odf(), conductance(), coverage(), cut_ratio(), density_ratio(), edges_inside(), expansion(), internal_density(), max_odf(), normalized_cut(), scoring_functions(), weighted_clustering_coefficient()

Examples

data(karate, package="igraphdata")
weighted_transitivity(karate)

---