Package 'netmem'

Title: Social Network Measures using Matrices
Description: Measures to describe and manipulate networks using matrices.
Authors: Alejandro Espinosa-Rada [cre, aut]
Maintainer: Alejandro Espinosa-Rada <[email protected]>
License: GPL-3 + file LICENSE
Version: 1.0-3
Built: 2025-03-11 14:56:37 UTC
Source: https://github.com/anespinosa/netmem

Help Index

Convert an Adjacency Matrix to an Incidence Matrix

Description

This function transforms an adjacency matrix into an incidence matrix.

Usage

adj_to_incidence(A, loops = TRUE, directed = TRUE, weighted = TRUE)

Arguments

A

A square numeric matrix representing the adjacency matrix of a graph. The matrix should have non-negative values, where 'A[i, j]' represents the weight of the edge from node 'i' to node 'j'.
loops

Logical. If 'TRUE', self-loops (edges from a node to itself) are included in the incidence matrix. If 'FALSE', they are removed. Default is 'TRUE'.
directed

Logical. If 'TRUE', the graph is treated as directed, meaning each edge has a specific source and target. If 'FALSE', the graph is treated as undirected, and edges are symmetrically represented. Default is 'TRUE'.
weighted

Logical. If 'TRUE', edge weights from 'A' are included in the incidence matrix. If 'FALSE', all edges are treated as having weight '1'. Default is 'TRUE'.

Value

A numeric matrix where rows represent nodes and columns represent edges. - In a **directed** network, a source node has a negative value (-weight), and a target node has a positive value (+weight). - In an **undirected** network, both nodes involved in an edge share the weight (positive values). - If 'weighted = FALSE', all edges have a weight of '1'.

Examples

# Define an adjacency matrix (directed and weighted)
A <- matrix(c(
  1, 3, 0, 0, 2,
  0, 0, 2, 0, 0,
  5, 0, 0, 0, 0,
  0, 0, 0, 0, 1,
  0, 4, 0, 0, 0
), byrow = TRUE, nrow = 5)

# Convert to an incidence matrix (directed, weighted)
(inc_matrix <- adj_to_incidence(A))

# Undirected, weighted graph
(inc_matrix_undirected <- adj_to_incidence(A, directed = FALSE))

# Directed, unweighted graph
(inc_matrix_unweighted <- adj_to_incidence(A, weighted = FALSE))

# Ignore loops
(inc_matrix_no_loops <- adj_to_incidence(A, loops = FALSE))

Transform an adjacency list into a matrix

Description

Transform an adjacency list into a matrix

Usage

adj_to_matrix(A, type = c("adjacency", "incidence", "weighted"), loops = FALSE)

Arguments

A

An adjacent list
type

Transform the adjacent list into an adjacency matrix, an incidence matrix or a weighted matrix
loops

Whether to include loops into the matrix

Value

This function transforms an adjacency list into a matrix

Author(s)

Alejandro Espinosa-Rada

Examples

adj_groups <- rbind(
  c("a", "b", "c"), c("a", "c", NA),
  c("b", "c", NA), c("c", NA, NA),
  c("c", "a", NA)
)
M <- adj_to_matrix(adj_groups, type = "adjacency", loops = TRUE)
M

Bonacich normalization

Description

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

Usage

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

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.

Source

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

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)

Clique table

Description

Exploration of a 3-cliques, as the maximum number of three or more actors who have all possible ties present among themselves

Usage

clique_table(A, list_cliques = FALSE, number = FALSE)

Arguments

A

A symmetric matrix object.
list_cliques

Whether to return the list of cliques.
number

Number of triangles

Value

This function return an edge list of actors participating in 3-cliques.

If list_cliques = TRUE it also return the list of cliques per nodes. If number = TRUE the output returns the number of 3-cliques in the matrix.

Author(s)

Alejandro Espinosa-Rada

References

Luce, R.D. and Perry, A.D. (1949). A method of matrix analysis of group structure. Psychometrika, 14: 95-116.

Roethlisberger, F.J. and Dickson, W.J. (1939). Management and the Worker. Harvard University Press, Cambridge, MA.

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

Examples

A <- matrix(c(
  0, 1, 1, 0, 0, 0, 0, 1, 0,
  1, 0, 1, 0, 0, 0, 0, 0, 0,
  1, 1, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 1, 1, 0, 0, 0,
  0, 0, 0, 1, 0, 0, 0, 0, 0,
  0, 0, 0, 1, 0, 0, 1, 1, 0,
  0, 0, 0, 0, 0, 1, 0, 1, 0,
  1, 0, 0, 0, 0, 1, 1, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0
), byrow = TRUE, ncol = 9)
rownames(A) <- letters[1:nrow(A)]
colnames(A) <- rownames(A)
clique_table(A, list_cliques = TRUE, number = TRUE)

Co‐occurrence

Description

Co‐occurrence matrix based on overlap function

Usage

co_ocurrence(
  A,
  similarity = c("ochiai", "cosine"),
  occurrence = TRUE,
  projection = FALSE
)

Arguments

A

A matrix
similarity

The similarities available are either Ochiai (default) or cosine.
occurrence

Whether to treat the matrix as a two-mode structure (a.k.a. rectangular matrix, occurrence matrix, affiliation matrix, bipartite network)
projection

Whether to apply a projection (inner product multiplication) to the matrix

Value

This function returns the normalisation of a matrix into a symmetrical co‐occurrence matrix

Author(s)

Alejandro Espinosa-Rada

References

Borgatti, S. P., Halgin, D. S., 2011. Analyzing affiliation networks. In: J. Scott and P. J. Carrington (Eds.) The Sage handbook of social network analysis (pp. 417-433), Sage.

Zhou, Q., & Leydesdorff, L. (2016). The normalization of occurrence and Co-occurrence matrices in bibliometrics using Cosine similarities and Ochiai coefficients. Journal of the Association for Information Science and Technology, 67(11), 2805–2814. https://doi.org/10.1002/asi.23603

Examples

A <- matrix(
  c(
    2, 0, 2,
    1, 1, 0,
    0, 3, 3,
    0, 2, 2,
    0, 0, 1
  ),
  nrow = 5, byrow = TRUE
)

co_ocurrence(A)

Components

Description

This function assigns an id to the components that each of the nodes of the matrix belongs

Usage

components_id(A)

Arguments

A

A matrix

Value

A vector assigning an id the components that each of the nodes of the matrix belongs

Author(s)

Alejandro Espinosa-Rada

References

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

Examples

A <- matrix(c(
  0, 1, 1, 0, 0,
  1, 0, 1, 0, 0,
  1, 1, 0, 0, 0,
  0, 0, 0, 0, 1,
  0, 0, 0, 1, 0
), byrow = TRUE, ncol = 5)
rownames(A) <- letters[1:ncol(A)]
colnames(A) <- rownames(A)
components_id(A)

Relational composition

Description

This function returns the relational composition of the given matrices. The compound relations define the paths and the social process flows of the given matrices (Pattison, 1993). However, those whom they link may or may not be aware of them. The compound relations allow us to identify "the possibly very long and devious chains of effects propagating withing concrete social systems through links of various kinds" (Lorrain & White, 1971: 50).

Usage

compound_relation(l = list(), comp = 3, matrices = FALSE, equate = FALSE)

Arguments

l

A list of matrices.
comp

A number with the length of paths to form the compound relation.
matrices

Whether to return the resulting matrices of the compound relations.
equate

Whether to return the semigroup equations.

Value

This function provides the composition or concatenation of compound relations and the primitives of the matrices.

Author(s)

Alejandro Espinosa-Rada

References

Boorman, Scott A. and White, Harrison C. (1976) Social Structure from Multiple Networks. II. Role Structures. American Journal of Sociology. 81(6): 1384-1446.

Lorrain, Francois and White, Harrison C. (1971) Structural Equivalence of Individuals in Social Networks. Journal of Mathematical Sociology. 1: 49-80

Pattison, Philippa (1993) Algebraic Models for Social Networks. Cambridge University Press.

Examples

A <- matrix(c(
  0, 1, 0, 0,
  1, 0, 0, 0,
  1, 1, 0, 1,
  0, 0, 1, 0
), byrow = TRUE, ncol = 4)
rownames(A) <- letters[1:NCOL(A)]
colnames(A) <- rownames(A)

B <- matrix(c(
  0, 1, 0, 0,
  1, 0, 0, 0,
  0, 0, 0, 1,
  0, 0, 1, 0
), byrow = TRUE, ncol = 4)
rownames(B) <- letters[1:NCOL(B)]
colnames(B) <- rownames(B)

cmp <- compound_relation(list(A, B), comp = 2, matrices = TRUE, equate = TRUE)
cmp$compound_relations
cmp$compound_matrices
cmp$equated

Cumulative sum of matrices

Description

Cumulative sum of matrices

Usage

cumulativeSumMatrices(matrixList)

Arguments

matrixList

A list of matrices

Value

This function returns the cumulative sum of matrices

Author(s)

Alejandro Espinosa-Rada

Examples

A <- matrix(c(
  0, 1, 1,
  0, 0, 0,
  0, 1, 0
), byrow = TRUE, ncol = 3)
B <- matrix(c(
  0, 0, 1,
  0, 0, 0,
  0, 0, 0
), byrow = TRUE, ncol = 3)
C <- matrix(c(
  0, 0, 0,
  1, 0, 0,
  0, 0, 0
), byrow = TRUE, ncol = 3)
matrixList <- list(A, B, C)
cumulativeSumMatrices(matrixList)

Geographical distances

Description

This function calculate some geographical distances considering a list of places specifying their latitud and longitud. The function currently works for degree decimal or radians formats.

Usage

dist_geographic(
  latitude,
  longitud,
  method = c("spherical", "harvesine", "manhattan", "minkowski"),
  places = NULL,
  dd_to_radians = FALSE,
  p = NULL
)

Arguments

latitude

A vector with latitude
longitud

A vector with longitud
method

Whether to use the Spherical Law of Cosines spherical (default), Haversine formula harvesine, Manhattan Distance manhattan or Minkoowski distance minkowski
places

A vector with the names of the places
dd_to_radians

Whether to transform degree decimal format to radians
p

Parameter p for the estimation of Minkowski distance (default = 2, which is equivalent to an Euclidian Distance)

Value

This function return a distance matrix.

Source

Adapted from Mario Pineda-Krch (Great-circle distance calculations in R)

Examples

set.seed(1234)
x <- cbind(latitud = rnorm(5, -90), longitud = rnorm(5, 45))
dist_geographic(x[, 1], x[, 2], method = "harvesine")

Structural similarities

Description

In the literature of social network, Euclidean distance (Burt, 1976) or correlations (Wasserman and Faust, 1994) were considered as measures of structural equivalence.

Usage

dist_sim_matrix(
  A,
  method = c("euclidean", "hamming", "jaccard"),
  bipartite = FALSE
)

Arguments

A

A matrix
method

The similarities/distance currently available are either Euclidean (default), Hamming, or Jaccard.
bipartite

Whether the object is an incidence matrix

Value

This function returns a distance matrix between nodes of the same matrix.

Author(s)

Alejandro Espinosa-Rada

References

Burt, Ronald S. (1976) Positions in networks. Social Forces, 55(1): 93-122.

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

Examples

A <- matrix(c(
  0, 1, 0, 0, 1,
  0, 0, 0, 1, 1,
  0, 1, 0, 0, 1,
  0, 0, 1, 1, 0,
  0, 1, 0, 0, 0
), nrow = 5, ncol = 5, byrow = TRUE)
rownames(A) <- letters[1:nrow(A)]
colnames(A) <- rownames(A)
dist_sim_matrix(A, method = "jaccard")

A <- matrix(c(
  0, 0, 3, 0, 5,
  0, 0, 2, 0, 4,
  5, 4, 0, 4, 0,
  0, 3, 0, 1, 0,
  0, 0, 0, 0, 2
), nrow = 5, ncol = 5, byrow = TRUE)
dist_sim_matrix(A, method = "euclidean")

Path distances

Description

Distances between nodes using breadth-first search (BFS) or Dijkstra's algorithm to find shortest path distances.

Usage

bfs_ugraph(A, from = NULL)

count_geodesics(A)

short_path(A, from = NULL, to = NULL)

wlocal_distances(A, select = c("all", "in", "out"), from, to, path = c())

wall_distances(A, select = c("all", "in", "out"))

Arguments

A

A symmetric matrix object
from

Node in which the path start
to

Node in which the path end
select

Whether to consider all sender and receiver ties of ego (all), only incoming ties (in), or outgoing ties (out). By default, all.
path

Path of the nodes

Value

This function returns the distances o shortest path distance between two nodes for unweighted graph (bfs_ugraph, count_geodesics and short_path respectively) and weighted graphs (wlocal_distances or wall_distances)

Author(s)

Alejandro Espinosa-Rada

References

Dijkstra, E. W. (1959). A note on two problems in connexion with graphs. Numerische Mathematik. 1: 269–271.

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)]

bfs_ugraph(A, from = "a")
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)]

count_geodesics(A)
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)]

short_path(A, from = "a", to = "d")
A <- matrix(
  c(
    0, 3, 3, 10, 15, 0, 0, 0,
    1, 0, 5, 2, 7, 0, 0, 0,
    3, 5, 0, 0, 0, 0, 0, 0,
    10, 2, 0, 0, 2, 7, 12, 0,
    11, 3, 0, 3, 0, 11, 2, 0,
    0, 0, 0, 7, 11, 0, 3, 2,
    0, 0, 0, 12, 2, 3, 0, 2,
    0, 0, 0, 0, 0, 2, 2, 0
  ),
  byrow = TRUE, ncol = 8, nrow = 8
)
rownames(A) <- c("a", "b", "s", "c", "d", "e", "f", "z")
colnames(A) <- rownames(A)
wlocal_distances(A, from = "a", to = "d")
A <- matrix(
  c(
    0, 3, 3, 10, 15, 0, 0, 0,
    1, 0, 5, 2, 7, 0, 0, 0,
    3, 5, 0, 0, 0, 0, 0, 0,
    10, 2, 0, 0, 2, 7, 12, 0,
    11, 3, 0, 3, 0, 11, 2, 0,
    0, 0, 0, 7, 11, 0, 3, 2,
    0, 0, 0, 12, 2, 3, 0, 2,
    0, 0, 0, 0, 0, 2, 2, 0
  ),
  byrow = TRUE, ncol = 8, nrow = 8
)
rownames(A) <- c("a", "b", "s", "c", "d", "e", "f", "z")
colnames(A) <- rownames(A)
wall_distances(A, select = "in")

Forbidden triad table

Description

This function explores dyads and triads (Simmel, 1950), building from the 'forbidden triad' (Granovetter, 1973). First, the minimum structure is an isolated node, then dyads. Afterwards, different combinations of 'forbidden triads' are explored.

Usage

dyad_triad_table(A, adjacency_list = FALSE, min = NULL, max = NULL)

Arguments

A

A symmetric matrix object.
adjacency_list

Whether to return the adjacency list of triads 201 per node.
min

Numeric constant, lower limit on the size of the triads 201 to find. NULL means no limit, ie. it is the same as 0.
max

Numeric constant, upper limit on the size of the triads 201 to find. NULL means no limit.

Value

This function return the list of triads that each node belong.

If adjacency_list = TRUE it also return the adjacency list of the 'forbidden triads' per node.

Author(s)

Alejandro Espinosa-Rada

References

Granovetter, M.S. (1973). The Strength of Weak Ties. American Journal of Sociology. 78 (6): 1360–80. https://doi.org/10.1086/225469.

Simmel, G. (1950). Individual and Society. In K. H. Wolff (Ed.), The Sociology of George Simmel. New York: Free Press.

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

Examples

A <- matrix(c(
  0, 1, 1, 1, 0,
  1, 0, 1, 0, 0,
  1, 1, 0, 0, 0,
  1, 0, 0, 0, 1,
  0, 0, 0, 1, 0
), byrow = TRUE, ncol = 5)
rownames(A) <- letters[1:nrow(A)]
colnames(A) <- letters[1:ncol(A)]

dyad_triad_table(A, adjacency_list = TRUE, min = 3)

Dyad census

Description

Dyad census

Usage

dyadic_census(G, directed = TRUE, loops = FALSE)

Arguments

G

A symmetric matrix object.
directed

Whether the matrix is directed or not
loops

Whether to expect nonzero elements in the diagonal of the matrix

Value

This function return the counts of the dyad census.

Author(s)

Alejandro Espinosa-Rada

References

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

Examples

data(krackhardt_friends)
dyadic_census(krackhardt_friends)

data(FIFAin)
dyadic_census(FIFAin[[1]], directed = FALSE)

Constraint

Description

Everett and Borgatti specification of the constraint measure for binary matrices

Usage

eb_constraint(A, ego = NULL, digraph = FALSE, weighted = FALSE)

Arguments

A

A symmetric matrix object
ego

Name of ego in the matrix
digraph

Whether the matrix is directed or undirected
weighted

Whether the matrix is weighted or not

Value

This function returns term 1, 2 and 3, the normalization and the maximum value of the specification of Everett and Borgatti (2020), and the constraint of Burt (1992).

Author(s)

Alejandro Espinosa-Rada

References

Burt, R.S., 1992. Structural Holes: the Social Structure of Competition. Harvard University Press, Cambridge.

Everett, M.G. and Borgatti, S., 2020. Unpacking Burt's constraint measure. Social Networks 62, pp. 50-57. doi: https://doi.org/10.1016/j.socnet.2020.02.001

Examples

A <- matrix(c(
  0, 1, 1, 0, 0, 1,
  1, 0, 1, 0, 0, 1,
  1, 1, 0, 0, 0, 1,
  0, 0, 0, 0, 1, 1,
  0, 0, 0, 1, 0, 1,
  1, 1, 1, 1, 1, 0
), ncol = 6, byrow = TRUE)

rownames(A) <- letters[1:nrow(A)]
colnames(A) <- letters[1:ncol(A)]
eb_constraint(A, ego = "f")

Transform an edgelist to a matrix

Description

Transform an edgelist to a matrix

Usage

edgelist_to_matrix(
  E,
  digraph = TRUE,
  label = NULL,
  label2 = NULL,
  bipartite = FALSE
)

Arguments

E

An edge list
digraph

Whether the matrix is directed or not
label

A vector with the names of the nodes
label2

A vector with the names of a different set of nodes
bipartite

Whether the matrix is bipartite

Value

This function transform the edgelist into a matrix

Author(s)

Alejandro Espinosa-Rada

Examples

A <- matrix(c(
  0, 1, 1, 0, 0, 0, 0, 1, 0,
  1, 0, 1, 0, 0, 0, 0, 0, 0,
  1, 1, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 1, 1, 0, 0, 0,
  0, 0, 0, 1, 0, 0, 0, 0, 0,
  0, 0, 0, 1, 0, 0, 1, 1, 0,
  0, 0, 0, 0, 0, 1, 0, 1, 0,
  1, 0, 0, 0, 0, 1, 1, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0
), byrow = TRUE, ncol = 9)
rownames(A) <- letters[1:nrow(A)]
colnames(A) <- rownames(A)
E <- matrix_to_edgelist(A)
edgelist_to_matrix(E, label = c("i"), digraph = FALSE)

Ego network

Description

Submatrix of ego's neighbourhoods

Usage

ego_net(
  A,
  ego = NULL,
  bipartite = FALSE,
  addEgo = FALSE,
  select = c("all", "in", "out")
)

Arguments

A

A symmetric matrix object
ego

Name of ego in the matrix
bipartite

Whether the matrix is a two-mode network
addEgo

Whether to retain ego in the submatrix or not
select

Whether to consider all sender and receiver ties of ego (all), only incoming ties (in), or outgoing ties (out). By default, all.

Value

This function returns redundancy, effective size and efficincy measures (Burt, 1992).

Author(s)

Alejandro Espinosa-Rada

References

Burt, R.S., 1992. Structural Holes: the Social Structure of Competition. Harvard University Press, Cambridge.

Borgatti, S., 1997. Unpacking Burt's redundancy measure. Connections, 20(1): 35-38. doi: http://www.analytictech.com/connections/v20(1)/holes.htm

Examples

A <- matrix(c(
  0, 1, 0, 0, 1, 1, 1,
  1, 0, 0, 1, 0, 0, 1,
  0, 0, 0, 0, 0, 0, 1,
  0, 1, 0, 0, 0, 0, 1,
  1, 0, 0, 0, 0, 0, 1,
  1, 0, 0, 0, 0, 0, 1,
  1, 1, 1, 1, 1, 1, 0
), ncol = 7, byrow = TRUE)
rownames(A) <- letters[1:nrow(A)]
colnames(A) <- letters[1:ncol(A)]
ego_net(A, ego = "g")

Krackhardt and Stern's E-I index

Description

This index was proposed by Krackhardt and Stern (1988) to distinguish between the relative prevalence of between and within-group ties. This measure can be interpreted as homophily at the network level.

Usage

ei_index(A, mixed = TRUE, att = NULL)

Arguments

A

A symmetric matrix object
mixed

Whether the matrix provided is already a mixed matrix or not
att

Categorical attribute of the nodes

Value

Numerical value of the E-I index.

Examples

set.seed(18051889)
n <- 100
A <- matrix(c(rbinom(n, 1, 0.5)),
  ncol = sqrt(n), nrow = sqrt(n), byrow = TRUE
)
rownames(A) <- letters[1:nrow(A)]
colnames(A) <- letters[1:ncol(A)]

att <- rbinom(sqrt(n), 3, 0.5)
ei_index(A, mixed = FALSE, att = att)

Expand Matrix

Description

Expand Matrix

Usage

expand_matrix(A, label = NULL, loops = FALSE, normalize = FALSE)

Arguments

A

A square matrix
label

Duplicated labels to expand the matrix
loops

Whether the loops are retained or not
normalize

Whether to normalize the matrix considering the fractional counting per group

Value

Return an expanded matrix

Author(s)

Alejandro Espinosa-Rada

Examples

A <- matrix(c(
  0, 1, 1,
  0, 0, 1,
  1, 0, 0
), byrow = TRUE, ncol = 3, nrow = 3)
rownames(A) <- letters[1:NROW(A)]
colnames(A) <- rownames(A)
label <- sort(rep(rownames(A), 2))
expand_matrix(A, label, loops = FALSE, normalize = TRUE)

Extract components

Description

This function extract the matrix of different components

Usage

extract_component(A, maximum = TRUE, position = NULL)

Arguments

A

A matrix
maximum

Whether to extract the maximum component
position

Whether to extract the component in the ith size position

Value

A matrix or a list of matrices with the required components

Author(s)

Alejandro Espinosa-Rada

References

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

Examples

A <- FIFAex$Matrix
rownames(A) <- FIFAex$label
colnames(A) <- rownames(A)
extract_component(A, maximum = TRUE)
extract_component(A, maximum = FALSE, position = 2)

Ego FIFA

Description

Multilevel Network of the regulatory transnational regime of the International Federation of Association Football (FIFA)

Usage

data(FIFAego)

Format

A list of a 48 x 48 symmetric matrix of the ego network of FIFA as a different entity, and a string vector with the label of the actors

Source

Espinosa, Alejandro & Ortiz, Francisca (2016). "Jurisdictional autonomy in the regulatory transnational regime of FIFA". REDES- Revista Hispana para el Analisis de Redes Sociales, 27(1), 100- 112. (Original title in Spanish: "Autonomia jurisdiccional en el reegimen regulatorio transnacional de la FIFAFA") <doi: https://doi.org/10.5565/rev/redes.595>

Outside FIFA

Description

Multilevel Network of the regulatory transnational regime of the International Federation of Association Football (FIFA)

Usage

data(FIFAex)

Format

A list of a 7 x 7 symmetric matrix of non-FIFA organizations, and a string vector with the label of the actors

Source

Espinosa, Alejandro & Ortiz, Francisca (2016). "Jurisdictional autonomy in the regulatory transnational regime of FIFA". REDES- Revista Hispana para el Analisis de Redes Sociales, 27(1), 100- 112. (Original title in Spanish: "Autonomia jurisdiccional en el reegimen regulatorio transnacional de la FIFAFA") <doi: https://doi.org/10.5565/rev/redes.595>#'

Inside FIFA

Description

Multilevel Network of the regulatory transnational regime of the International Federation of Association Football (FIFA)

Usage

data(FIFAin)

Format

A list of a 41 x 41 symmetric matrix of roles and organizations inside FIFA, and a string vector with the label of the actors

Source

Espinosa, Alejandro & Ortiz, Francisca (2016). "Jurisdictional autonomy in the regulatory transnational regime of FIFA". REDES- Revista Hispana para el Analisis de Redes Sociales, 27(1), 100- 112. (Original title in Spanish: "Autonomia jurisdiccional en el reegimen regulatorio transnacional de la FIFAFA") <doi: https://doi.org/10.5565/rev/redes.595>

Fractional approach

Description

Matrix transformation from incidence matrices to citation networks, fractional counting for co-citation or fractional counting for bibliographic coupling

Usage

fractional_approach(
  A1,
  A2,
  approach = c("citation", "cocitation", "bcoupling")
)

Arguments

A1

From incidence matrix (e.g. paper and authors)
A2

To incidence matrix (e.g. author to paper)
approach

Character string, “citation”, “cocitation” and “bcoupling”

Value

Return a type of "citation network"

Author(s)

Alejandro Espinosa-Rada

References

Batagelj, V. (2020). Analysis of the Southern women network using fractional approach. Social Networks, 68, 229-236 https://doi.org/10.1016/j.socnet.2021.08.001

Batagelj, V., & Cerinšek, M. (2013). On bibliographic networks. Scientometrics, 96(3), 845–864. https://doi.org/10.1007/s11192-012-0940-1

Examples

A1 <- matrix(c(
  1, 0, 0, 0,
  0, 1, 0, 0,
  0, 1, 1, 1,
  0, 0, 0, 0,
  0, 0, 0, 1
), byrow = TRUE, ncol = 4)

A2 <- matrix(c(
  1, 1, 1, 0, 0,
  0, 0, 1, 0, 0,
  0, 0, 1, 1, 0,
  0, 0, 0, 1, 1
), byrow = TRUE, ncol = 5)

fractional_approach(A1, A2)

Generalized degree

Description

Generalized degree centrality for one-mode and bipartite networks

Usage

gen_degree(
  A,
  weighted = FALSE,
  type = "out",
  normalized = FALSE,
  loops = TRUE,
  digraph = TRUE,
  alpha = 0.5,
  bipartite = FALSE
)

Arguments

A

A matrix object
weighted

Whether the matrix is weighted or not
type

Character string, “out” (outdegree), “in” (indegree) and “all” (degree)
normalized

Whether normalize the measure for the one-mode network (Freeman, 1978) or a bipartite network (Borgatti and Everett, 1997)
loops

Whether the diagonal of the matrix is considered or not
digraph

Whether the matrix is directed or undirected
alpha

Sets the alpha parameter in the generalised measures from Opsahl et al. (2010)
bipartite

Whether the matrix is bipartite or not.

Value

This function returns term 1, 2 and 3, the normalization and the maximum value of the specification of Everett and Borgatti (2020), and the constraint of Burt (1992)

Author(s)

Alejandro Espinosa-Rada

References

Borgatti, S. P., and Everett, M. G. (1997). Network analysis of 2-mode data. Social Networks, 19(3), 243–269.

Freeman, L. C. (1978). Centrality in social networks conceptual clarification. Social Networks, 1(3), 215–239.

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

Examples

A3 <- matrix(c(
  0, 4, 4, 0, 0, 0,
  4, 0, 2, 1, 1, 0,
  4, 2, 0, 0, 0, 0,
  0, 1, 0, 0, 0, 0,
  0, 1, 0, 0, 0, 7,
  0, 0, 0, 0, 7, 0
), byrow = TRUE, ncol = 6)

gen_degree(A3, digraph = FALSE, weighted = TRUE)

Generalized density

Description

Generalized density

Usage

gen_density(
  A,
  directed = TRUE,
  bipartite = FALSE,
  loops = FALSE,
  weighted = FALSE,
  multilayer = FALSE
)

Arguments

A

A symmetric or incidence matrix object
directed

Whether the matrix is directed
bipartite

Whether the matrix is bipartite
loops

Whether to consider the loops
weighted

Whether the matrix is weighted
multilayer

Whether the matrix is multilayer (i.e., multiplex and/or multilevel)

Value

This function returns the density of the matrix(es)

Author(s)

Alejandro Espinosa-Rada

References

Wasserman, S., and Faust, K. (1994). Social Network Analysis: Methods and Applications. Cambridge: Cambridge University Press.

Examples

# A bipartite matrix
B <- matrix(c(
  1, 1, 0,
  0, 0, 1,
  0, 1, 1,
  0, 0, 1
), byrow = TRUE, ncol = 3)
gen_density(B, bipartite = TRUE)

# A multilevel network
A1 <- matrix(c(
  0, 1, 0, 0, 1,
  1, 0, 0, 1, 1,
  0, 0, 0, 1, 1,
  0, 1, 1, 0, 1,
  1, 1, 1, 1, 0
), byrow = TRUE, ncol = 5)

B1 <- matrix(c(
  1, 0, 0,
  1, 1, 0,
  0, 1, 0,
  0, 1, 0,
  0, 1, 1
), byrow = TRUE, ncol = 3)

A2 <- matrix(c(
  0, 1, 1,
  1, 0, 0,
  1, 0, 0
), byrow = TRUE, nrow = 3)

B2 <- matrix(c(
  1, 1, 0, 0,
  0, 0, 1, 0,
  0, 0, 1, 1
), byrow = TRUE, ncol = 4)

A3 <- matrix(c(
  0, 1, 3, 1,
  1, 0, 0, 0,
  3, 0, 0, 5,
  1, 0, 5, 0
), byrow = TRUE, ncol = 4)

matrices <- list(A1, B1, A2, B2, A3)
gen_density(matrices, multilayer = TRUE)

# A multiplex network
A <- matrix(c(
  0, 1, 3, 6, 4,
  2, 0, 4, 5, 2,
  4, 1, 0, 6, 1,
  5, 6, 3, 0, 6,
  1, 1, 2, 3, 0
), byrow = TRUE, ncol = 5)
gen_density(A, multilayer = TRUE)

Blau's and IQV index

Description

This index was used by Blau (1977) to distinguish between the relative prevalence of between and within-group ties. This measure can be interpreted as heterogeneity at the network level.

Usage

heterogeneity(att, normalized = FALSE)

Arguments

att

Categorical attribute of the nodes
normalized

Whether to return IQV index

Value

Numerical value of the Blau index.

If normalized = TRUE, then the function also return IQV index.

References

Agresti, A. and Agresti, B. (1978). Statistical Analysis of Qualitative Variation. Sociological Methodology, 9, 204-237. doi: https://doi.org/10.2307/270810

Blau, P. M. (1977). Inequality and heterogeneity. New York: Free Press.

Examples

a <- rep(1:10, 10)
heterogeneity(a, normalized = TRUE)

a <- rep(1:2, 10)
heterogeneity(a, normalized = TRUE)

Hypergraphs

Description

Hypergraph consist of a set of objects and a collection of subsets of objects, in which each object belongs to at least one subset, and no subset is empy (Berge, 1989)

Usage

hypergraph(A, dual = TRUE, both = TRUE)

Arguments

A

An incidence matrix.
dual

Whether to return the dual hypergraph (which rever the role of the pointes and the edges)
both

Whether to return the hypergraph and the dual hypergraph

Value

This function returns an adjacent list of the subsets of entities in the hypergraph.

Author(s)

Alejandro Espinosa-Rada

References

Berge, C. (1973). Graphs and hypergraphs.Amsterdam: North-Holland.

Berge, C. (1989). Hypergraphs: Combinatorics of finite sets. Amsterdam: North-Holland.

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

Examples

A <- matrix(c(
  1, 0, 1,
  0, 1, 0,
  0, 1, 1,
  0, 0, 1,
  1, 1, 1,
  1, 1, 0
), byrow = TRUE, ncol = 3)
colnames(A) <- letters[1:ncol(A)]
rownames(A) <- letters[(ncol(A) + 1):(nrow(A) + ncol(A))]
hypergraph(A, both = TRUE)

Independent random matrix

Description

The function creates random matrices following a uniform probability over the space of networks having exactly m fixed number of edges (Moreno and Jennings, 1938; Rapoport, 1948; Solomonoff and Rapoport, 1951; Erdos and Renyi, 1959) or following a probability of the formation of the ties (Gilbert, 1959) assuming ties independency.

Usage

ind_rand_matrix(
  n,
  m = NULL,
  type = c("edges", "probability"),
  digraph = TRUE,
  loops = FALSE,
  l = NULL,
  p = NULL,
  trials = 1,
  multilevel = FALSE
)

Arguments

n

The number of nodes of the first set
m

The number of nodes of a second set
type

The model assumes a fixed number of edges model (a.k.a. G(n,m)) (default) or a probability model (a.k.a. G(n,p))
digraph

Whether the matrix is symmetric or not
loops

Whether to expect nonzero elements in the diagonal of the matrix
l

The number of ties expected for the edges (a.k.a. G(n,m)) model
p

The probability of the ties expected for the probability (a.k.a. G(n,p)) model. If no parameter 'p' is specified, a uniform distribution is considered (p=0.5).
trials

Whether to add counting numbers to the probability (a.k.a. G(n,p)) model
multilevel

Whether to return a meta-matrix to represent a multilevel network

Details

The fixed model is often called the G(n,m) graph with 'n' nodes and 'm' edges, and the 'm' edges are chosen uniformly randomly from the set of all possible ties.

The probability model is known as the G(n,p) graph, in which the matrix has 'n' nodes, and for each tie, the probability that it is present in the matrix is 'p'.

These are the simplest models that follow a conditional uniform distribution that place nonnull probability on a subset of networks with distinctive characteristics corresponding to the observed networks - for example, simulating a matrix based on the number of ties observed in the network.

Value

This function return the counts of the dyad census.

Author(s)

Alejandro Espinosa-Rada

References

Erdos, P. and Renyi, A. (1959). On random graphs. Publicationes Mathematicae 6, 290–297.

Gilbert, N. (1959). Random Graphs. The Annals of Mathematical Statistics, 30(4): 1141-1144.

Moreno, J. and Jennings, H. (1938). Statistics of social configurations. Sociometry, 1(3/4):342–374.

Rapoport, A. (1948). Cycle distributions in random nets. Bulletin of Mathematical Biology, 10(3):145–157.

Solomonoff, R. and Rapoport, A. (1951). Connectivity of random nets. Bulletin of Mathematical Biology, 13:107–117.

Examples

set.seed(18051889)
ind_rand_matrix(5, type = "edges", l = 3, digraph = TRUE, loops = TRUE)
ind_rand_matrix(5, type = "probability")
ind_rand_matrix(n = 5, m = 2, p = 0.20, type = "probability", multilevel = TRUE)

Jaccard similarity

Description

Jaccard similarity identifies the changes of ties between two matrices.

Usage

jaccard(
  A,
  B,
  directed = TRUE,
  diag = FALSE,
  coparticipation = FALSE,
  bipartite = FALSE
)

Arguments

A

Binary matrix A
B

Binary matrix B
directed

Whether the matrix is symmetric
diag

Whether the diagonal should be considered
coparticipation

Select nodes that co-participate in both matrices
bipartite

Whether the matrix is incidence

Value

The output are: jaccard = Jaccard similarity, proportion = proportion among the ties present at a given observation of ties that are also present in the other matrix, and table = a table with the tie changes between matrices.

If coparticipation = TRUE, then also: match = The number of nodes present in both matrices; size_matrix1 = The size of the first matrix; size_matrix2 = The size of the second matrix; coparticipation1 = The percentage of nodes in the first matrix also present in the second matrix; coparticipation2 = The percentage of nodes in the second matrix also present in the first matrix: overlap_actors = Overlap of nodes between two matrices

#' If coparticipation = TRUE and bipartite = TRUE, then also: matchM1 = The number of nodes in the first 'mode' present in both matrices; matchM2 = The number of nodes in the second 'mode' present in both matrices; size_matrix1_M1 = The number of nodes in the first 'mode' of the first matrix; size_matrix1_M2 = The number of nodes in the second 'mode' of the first matrix; size_matrix2_M1 = The number of nodes in the first 'mode' of the second matrix; size_matrix2_M2 = The number of nodes in the second 'mode' of the second matrix; coparticipation1_M2 = The percentage of nodes of the first 'mode' in the first matrix present in the second matrix. coparticipation1_M2 = The percentage of nodes of the second 'mode' in the first matrix present in the second matrix. coparticipation2_M1 = The percentage of nodes of the first 'mode' in the second matrix present in the first matrix. coparticipation2_M2 = The percentage of nodes of the second 'mode' in the second matrix present in the first matrix. overlap_actors_M1 = Overlap between two matrices (nodes of the first 'mode') overlap_actors_M2 = Overlap between two matrices (nodes of the second 'mode')

Author(s)

Alejandro Espinosa-Rada

References

Batagelj, V., and Bren, M. (1995). Comparing resemblance measures. Journal of Classification 12, 73–90.

Examples

A <- matrix(c(
  0, 1, 1, 0,
  1, 0, 0, 0,
  1, 0, 0, 0,
  0, 0, 1, 0
), byrow = TRUE, ncol = 4)
B <- matrix(c(
  0, 1, 1, 0,
  1, 0, 0, 0,
  1, 0, 0, 0,
  0, 0, 0, 0
), byrow = TRUE, ncol = 4)
jaccard(A, B, directed = TRUE)

Generalized k-core

Description

Generalized k-core for undirected, directed, weighted and multilevel networks

Usage

k_core(
  A,
  B1 = NULL,
  multilevel = FALSE,
  type = "in",
  digraph = FALSE,
  loops = FALSE,
  weighted = FALSE,
  alpha = 1
)

Arguments

A

A matrix object.
B1

An incidence matrix for multilevel networks.
multilevel

Whether the measure of k-core is for multilevel networks.
type

Character string, “out” (outdegree), “in” (indegree) and “all” (degree)
digraph

Whether the matrix is directed or undirected
loops

Whether the diagonal of the matrix is considered or not
weighted

Whether the measure of k-core is for valued matrices
alpha

Sets the alpha parameter in the generalised measures from Opsahl et al. (2010)

Value

This function return the k-core.

Author(s)

Alejandro Espinosa-Rada

References

Batagelj, V., & Zaveršnik, M. (2011). Fast algorithms for determining (generalized) core groups in social networks. Advances in Data Analysis and Classification, 5(2), 129–145. https://doi.org/10.1007/s11634-010-0079-y

Eidsaa, M., & Almaas, E. (2013). s-core network decomposition: A generalization of $k$-core analysis to weighted networks. Physical Review E, 88(6), 062819. https://doi.org/10.1103/PhysRevE.88.062819

Seidman S (1983). 'Network structure and minimum degree'. Social Networks, 5, 269-287.

Examples

A1 <- matrix(c(
  0, 1, 0, 0, 0,
  1, 0, 0, 1, 0,
  0, 0, 0, 1, 0,
  0, 1, 1, 0, 1,
  0, 0, 0, 1, 0
), byrow = TRUE, ncol = 5)
B1 <- matrix(c(
  1, 0, 0,
  1, 1, 0,
  0, 1, 0,
  0, 1, 0,
  0, 1, 1
), byrow = TRUE, ncol = 3)

k_core(A1, B1, multilevel = TRUE)

Reciprocity of Katz and Powell

Description

Reciprocity of Katz and Powell

Usage

kp_reciprocity(G, fixed = FALSE, d = NULL, dichotomic = TRUE)

Arguments

G

A symmetric matrix object.
fixed

Whether the choices are fixed or not
d

Numeric value of the number of fixed choices.
dichotomic

Whether the matrix is weighted or binary

Value

This function gives a measurment of the tendency toward reciprocation of choices.

Author(s)

Alejandro Espinosa-Rada

References

Katz, L. and Powell, J.H. (1955). "Measurement of the tendency toward reciprocation of choice." Sociometry, 18:659-665.

Examples

data(krackhardt_friends)
kp_reciprocity(krackhardt_friends, fixed = TRUE, d = 5)

Krackhardt friends

Description

Friendship network of the relations measured for Krackhardt's high-tech managers.

Usage

data(krackhardt_friends)

Format

A 21 x 21 directed matrix of the managers

Source

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

Lazega law firm

Description

The data is part of a study carried out in a Northeastern US corporate law firm, referred to as SG&R, 1988-1991 in New England. The data were collected by Emmanuel Lazega (2001). This is a multiplex network of attorneys (partners and associates) of this firm. It includes (among others) measurements of networks among the 71 attorneys (partners and associates) of this firm, i.e. their strong-coworker network, advice network, friendship network, and indirect control networks.

Usage

data(lazega_lawfirm)

Format

Three 71 X 71 matrices:

cowork

A matrix indicating "cowork" relationships among the attorneys, based on their work together on cases and other professional activities.

advice

A matrix indicating "advice" relationships, where the matrix shows to whom attorneys went for professional advice.

friends

A matrix indicating "friends" relationships, showing social connections outside of work.

attributes

A data frame with attributes of the actors, including:

seniority

Seniority.

status

1=partner; 2=associate

gender

1=man; 2=woman

office

1=Boston; 2=Hartford; 3=Providence

years

Years with the firm

age

Age

practice

1=litigation; 2=corporate

law_school

1 = Harvard, Yale; 2 = UConn; 3 = Other

Source

Lazega, Emmanuel (2001) The Collegial Phenomenon: The Social Mechanisms of Cooperation Among Peers in a Corporate Law Partnership. Oxford University Press.

Transform a matrix to an adjacency list

Description

Transform a matrix to an adjacency list

Usage

matrix_adjlist(A)

Arguments

A

A matrix

Value

This function transform a matrix to an adjacency list

Author(s)

Alejandro Espinosa-Rada

Examples

A <- matrix(c(
  0, 1, 1, 0, 0, 0, 0, 1, 0,
  1, 0, 1, 0, 0, 0, 0, 0, 0,
  1, 1, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 1, 1, 0, 0, 0,
  0, 0, 0, 1, 0, 0, 0, 0, 0,
  0, 0, 0, 1, 0, 0, 1, 1, 0,
  0, 0, 0, 0, 0, 1, 0, 1, 0,
  1, 0, 0, 0, 0, 1, 1, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0
), byrow = TRUE, ncol = 9)
rownames(A) <- letters[1:nrow(A)]
colnames(A) <- rownames(A)
matrix_adjlist(A)

Unipartite projections

Description

Two-mode networks can be represented (or 'projected') as one-mode networks.

Usage

matrix_projection(A, B = NULL, digraph = FALSE)

Arguments

A

A first matrix object
B

A second matrix object
digraph

Whether the matrix is directed or not

Value

This function return a list of matrices of the two projections of the original matrix.

Author(s)

Alejandro Espinosa-Rada

References

Davis, Allison; Gardner, Burleigh B. and Mary. R. Gardner (1941). Deep South: A Social Anthropological Study of Caste and Class. The University of Chicago Press, Chicago.

Breiger, Ronald L. (1976). The Duality of Persons and Groups, 53(2), 181-190 doi: https://doi.org/10.2307/2576011

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

Examples

A <- matrix(c(
  2, 0, 2,
  1, 1, 0,
  0, 3, 3,
  0, 2, 2,
  0, 0, 1
), byrow = TRUE, ncol = 3)
matrix_projection(A)

A <- matrix(c(
  0, 0, 0, 0, 1,
  1, 0, 0, 0, 0,
  1, 1, 0, 0, 0,
  0, 1, 1, 1, 1,
  0, 0, 1, 0, 0,
  0, 0, 1, 1, 0
), byrow = TRUE, ncol = 5)

B <- matrix(c(
  0, 0, 0, 0, 1,
  1, 0, 0, 0, 0,
  1, 0, 0, 0, 0,
  0, 1, 0, 0, 0,
  0, 0, 1, 0, 0,
  0, 0, 1, 0, 0
), byrow = TRUE, ncol = 5)
matrix_projection(A, B, digraph = TRUE)

Matrix report

Description

The primary matrix used in social network analysis are the adjacency matrix or sociomatrix, and the incidence matrix.

Usage

matrix_report(A)

Arguments

A

A matrix

Value

This function return a report of some of the characteristics of the matrix.

Author(s)

Alejandro Espinosa-Rada

References

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

Examples

A <- matrix(c(
  1, 1, 0, 0, -1,
  1, 0, 0, 1, 1,
  0, 0, NA, 1, 1,
  0, 1, 1, 0, 1,
  1, 1, 1, 1, 0
), byrow = TRUE, ncol = 5)

B <- matrix(c(
  1, 0, 0,
  1, 1, 0,
  0, NA, 0,
  0, 1, 0,
  0, 1, 1
), byrow = TRUE, ncol = 3)
matrix_report(A)
matrix_report(B)

Transform a square matrix to an edge-list

Description

Transform a square matrix to an edge-list

Usage

matrix_to_edgelist(A, digraph = FALSE, valued = FALSE, loops = FALSE)

Arguments

A

A square matrix
digraph

Whether the matrix is directed or not
valued

Add a third columns with the valued of the relationship
loops

Whether the loops are retained or not

Value

This function transform the matrix into an edgelist

Author(s)

Alejandro Espinosa-Rada

Examples

A <- matrix(c(
  0, 2, 1,
  1, 0, 0,
  1, 0, 1
), byrow = TRUE, ncol = 3)
matrix_to_edgelist(A, digraph = TRUE, valued = TRUE, loops = TRUE)

Meta matrix for multilevel networks

Description

Meta matrix for multilevel networks

Usage

meta_matrix(A1, B1, A2 = NULL, B2 = NULL, A3 = NULL, B3 = NULL)

Arguments

A1

The square matrix of the lowest level
B1

The incidence matrix of the ties between the nodes of first level and the nodes of the second level
A2

The square matrix of the second level
B2

The incidence matrix of the ties between the nodes of the second level and the nodes of the third level
A3

The square matrix of the third level
B3

The incidence matrix of the ties between the nodes of the third level and the nodes of the first level

Value

Return a meta matrix for multilevel networks

Author(s)

Alejandro Espinosa-Rada

References

Carley, K. M. (2002). Smart agents and organizations of the future. In: Leah Lievrouw & Sonia Livingstone (Eds.), The Handbook of New Media (pp. 206-220). Thousand Oaks, CA, Sage.

Krackhardt, D., & Carley, K. M. (1998). PCANS model of structure in organizations (pp. 113- 119). Pittsburgh, Pa, USA: Carnegie Mellon University, Institute for Complex Engineered Systems.

Examples

A1 <- matrix(c(
  0, 1, 0, 0, 0,
  1, 0, 0, 1, 0,
  0, 0, 0, 1, 0,
  0, 1, 1, 0, 1,
  0, 0, 0, 1, 0
), byrow = TRUE, ncol = 5)

B1 <- matrix(c(
  1, 0, 0,
  1, 1, 0,
  0, 1, 0,
  0, 1, 0,
  0, 1, 1
), byrow = TRUE, ncol = 3)

A2 <- matrix(c(
  0, 1, 1,
  1, 0, 0,
  1, 0, 0
), byrow = TRUE, nrow = 3)

B2 <- matrix(c(
  1, 1, 0, 0,
  0, 0, 1, 0,
  0, 0, 1, 1
), byrow = TRUE, ncol = 4)

A3 <- matrix(c(
  0, 1, 1, 1,
  1, 0, 0, 0,
  1, 0, 0, 1,
  1, 0, 1, 0
), byrow = TRUE, ncol = 4)

B3 <- matrix(c(
  1, 0, 0, 0, 0,
  0, 1, 0, 1, 0,
  0, 0, 0, 0, 0,
  0, 0, 0, 0, 0
), byrow = TRUE, ncol = 5)

rownames(A1) <- letters[1:nrow(A1)]
colnames(A1) <- rownames(A1)
rownames(A2) <- letters[nrow(A1) + 1:nrow(A2)]
colnames(A2) <- rownames(A2)
rownames(B1) <- rownames(A1)
colnames(B1) <- colnames(A2)
rownames(A3) <- letters[nrow(A1) + nrow(A2) + 1:nrow(A3)]
colnames(A3) <- rownames(A3)
rownames(B2) <- rownames(A2)
colnames(B2) <- colnames(A3)
rownames(B3) <- rownames(A3)
colnames(B3) <- rownames(A1)
meta_matrix(A1, B1, A2, B2, A3, B3)

Minimum/maximum overlap

Description

Two-mode networks can be represented (or 'projected') as one-mode networks.

Usage

minmax_overlap(A, row = TRUE, min = TRUE)

Arguments

A

A matrix object
row

Whether to consider the actors in the rows of the matrix (default) or the column.
min

Whether to extract the minimum (default) or the maximum overlap.

Value

This function return the overlap between the modes (a.k.a. actors, nodes, vertices).

Author(s)

Alejandro Espinosa-Rada

References

Morris, S.A. (2005). Unified Mathematical Treatment of Complex Cascaded Bipartite Networks: The Case of Collections of Journal Papers. Unpub- lished PhD Thesis, Oklahoma State University. Retrieved from http://digital.library.okstate.edu/etd/umi-okstate-1334.pdf

Examples

A <- matrix(c(
  2, 0, 2,
  1, 1, 0,
  0, 3, 3,
  0, 2, 2,
  0, 0, 1
), byrow = TRUE, ncol = 3)
minmax_overlap(A)

Mixing matrix

Description

Create a mixing matrix from node attributes. The mixing matrix is a two-dimensional matrix that cross-classifies the edges depending on the values of their attributes. This matrix allowed identifying segregation and homophily at the network level.

Usage

mix_matrix(A, att = NULL)

Arguments

A

A symmetric matrix object
att

Categorical attribute of the nodes

Details

Values in the diagonal are the number of ties within groups, and off-diagonal are the number of relations between groups.

Value

This function returns a mixing matrix.

Author(s)

Alejandro Espinosa-Rada

Examples

n <- 100
A <- matrix(c(rbinom(n, 1, 0.5)),
  ncol = sqrt(n), nrow = sqrt(n), byrow = TRUE
)
rownames(A) <- letters[1:nrow(A)]
colnames(A) <- letters[1:ncol(A)]
att <- rbinom(sqrt(n), 3, 0.5)
mix_matrix(A, att = att)

Multilevel triad and quadrilateral census

Description

Multilevel triad and quadrilateral census

Usage

mixed_census(A1, B1, B2 = NULL, quad = FALSE)

Arguments

A1

An adjacent matrix object.
B1

An incidence matrix object.
B2

An incidence matrix object.
quad

Whether the matrix is a quadrilateral census or not.

Value

This function return the counts of a multilevel census.

If quad = TRUE, then the function return the multilevel quadrilateral census.

Author(s)

Alejandro Espinosa-Rada

References

Espinosa-Rada, A. (2021). A Network Approach for the Sociological Study of Science: Modelling Dynamic Multilevel Networks. [PhD](https://research.manchester.ac.uk/en/studentTheses/a-network-approach-for-the-sociological-study-of-science-and-know). The University of Manchester.

Espinosa-Rada, A., Bellotti, E., Everett, M., & Stadtfeld, C. (2024). Co-evolution of a socio-cognitive scientific network: A case study of citation dynamics among astronomers. Social Networks, 78, 92–108. https://doi.org/10.1016/j.socnet.2023.11.008

Hollway, J., Lomi, A., Pallotti, F., & Stadtfeld, C. (2017). Multilevel social spaces: The network dynamics of organizational fields. Network Science, 5(2), 187–212. https://doi.org/10.1017/nws.2017.8

Examples

B1 <- matrix(c(
  1, 1, 0,
  0, 0, 1,
  0, 0, 1,
  1, 0, 0
), byrow = TRUE, ncol = 3)
A1 <- matrix(c(
  0, 1, 0, 1,
  1, 0, 0, 1,
  0, 1, 0, 1,
  1, 0, 1, 0
), byrow = TRUE, ncol = 4)
B2 <- matrix(c(
  1, 0, 0, 0, 0,
  0, 1, 0, 1, 0,
  0, 0, 0, 0, 0,
  0, 0, 0, 0, 0
), byrow = TRUE, ncol = 5)

mixed_census(A1, B1, B2, quad = TRUE)

Degree centrality for multilevel networks

Description

Degree centrality for multilevel networks

Usage

multilevel_degree(
  A1,
  B1,
  A2 = NULL,
  B2 = NULL,
  A3 = NULL,
  B3 = NULL,
  complete = FALSE,
  digraphA1 = FALSE,
  digraphA2 = FALSE,
  digraphA3 = FALSE,
  typeA1 = "out",
  typeA2 = "out",
  typeA3 = "out",
  loopsA1 = FALSE,
  loopsA2 = FALSE,
  loopsA3 = FALSE,
  normalized = FALSE,
  weightedA1 = FALSE,
  weightedA2 = FALSE,
  weightedA3 = FALSE,
  alphaA1 = 0.5,
  alphaA2 = 0.5,
  alphaA3 = 0.5
)

Arguments

A1

The square matrix of the lowest level
B1

The incidence matrix of the ties between the nodes of first level and the nodes of the second level
A2

The square matrix of the second level
B2

The incidence matrix of the ties between the nodes of the second level and the nodes of the third level
A3

The square matrix of the third level
B3

The incidence matrix of the ties between the nodes of the third level and the nodes of the first level
complete

Add the degree of bipartite and tripartite networks for B1, B2 and/or B3, and the low_multilevel (i.e. A1+B1+B2+B3), meso_multilevel (i.e. B1+A2+B2+B3) and high_multilevel (i.e. B1+B2+A3+B3) degree
digraphA1

Whether A1 is a directed network
digraphA2

Whether A2 is a directed network
digraphA3

Whether A3 is a directed network
typeA1

Type of degree of the network for A1, "out" for out-degree, "in" for in-degree or "all" for the sum of the two
typeA2

Type of degree of the network for A2, "out" for out-degree, "in" for in-degree or "all" for the sum of the two
typeA3

Type of degree of the network for A3, "out" for out-degree, "in" for in-degree or "all" for the sum of the two
loopsA1

Whether the loops of the edges are considered in matrix A1
loopsA2

Whether the loops of the edges are considered in matrix A2
loopsA3

Whether the loops of the edges are considered in matrix A3
normalized

If TRUE then the result is divided by (n-1)+k+m for the first level, (m-1)+n+k for the second level, and (k-1)+m+n according to Espinosa-Rada et al. (2021)
weightedA1

Whether A1 is weighted
weightedA2

Whether A2 is weighted
weightedA3

Whether A3 is weighted
alphaA1

The alpha parameter of A1 according to Opsahl et al (2010) for weighted networks. The value 0.5 is given by default.
alphaA2

The alpha parameter of A2 according to Opsahl et al (2010) for weighted networks. The value 0.5 is given by default.
alphaA3

The alpha parameter of A3 according to Opsahl et al (2010) for weighted networks. The value 0.5 is given by default.

Value

Return a data.frame of multilevel degree

Author(s)

Alejandro Espinosa-Rada

References

Borgatti, S. P., and Everett, M. G. (1997). Network analysis of 2-mode data. Social Networks, 19(3), 243–269.

Freeman, L. C. (1978). Centrality in social networks conceptual clarification. Social Networks, 1(3), 215–239.

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

Examples

A1 <- matrix(c(
  0, 1, 0, 0, 0,
  1, 0, 0, 1, 0,
  0, 0, 0, 1, 0,
  0, 1, 1, 0, 1,
  0, 0, 0, 1, 0
), byrow = TRUE, ncol = 5)

B1 <- matrix(c(
  1, 0, 0,
  1, 1, 0,
  0, 1, 0,
  0, 1, 0,
  0, 1, 1
), byrow = TRUE, ncol = 3)

A2 <- matrix(c(
  0, 1, 1,
  1, 0, 0,
  1, 0, 0
), byrow = TRUE, nrow = 3)

B2 <- matrix(c(
  1, 1, 0, 0,
  0, 0, 1, 0,
  0, 0, 1, 1
), byrow = TRUE, ncol = 4)

A3 <- matrix(c(
  0, 1, 1, 1,
  1, 0, 0, 0,
  1, 0, 0, 1,
  1, 0, 1, 0
), byrow = TRUE, ncol = 4)

B3 <- matrix(c(
  1, 0, 0, 0, 0,
  0, 1, 0, 1, 0,
  0, 0, 0, 0, 0,
  0, 0, 0, 0, 0
), byrow = TRUE, ncol = 5)

multilevel_degree(A1, B1, A2, B2, A3, B3)
## Not run: 
multilevel_degree(A1, B1, A2, B2, A3, B3, normalized = TRUE, complete = TRUE)

## End(Not run)

Multiplex triad census

Description

This function counts the different subgraphs of three nodes in a multiplex directed and undirected network.

Usage

multiplex_census(A, B)

Arguments

A

A directed matrix object.
B

An undirected matrix object.

Value

This function gives the counts of the mixed multiplex triad census for a directed and an undirected network.

Author(s)

Alejandro Espinosa-Rada

References

Espinosa-Rada, A. (2021). A Network Approach for the Sociological Study of Science: Modelling Dynamic Multilevel Networks. [PhD](https://research.manchester.ac.uk/en/studentTheses/a-network-approach-for-the-sociological-study-of-science-and-know). The University of Manchester.

Espinosa-Rada, A., Bellotti, E., Everett, M., & Stadtfeld, C. (2024). Co-evolution of a socio-cognitive scientific network: A case study of citation dynamics among astronomers. Social Networks, 78, 92–108. https://doi.org/10.1016/j.socnet.2023.11.008

Examples

# SOAR
A <- matrix(
  c(
    0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1,
    0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0,
    0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1,
    0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
    0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
  ),
  byrow = TRUE, ncol = 12
)

B <- matrix(
  c(
    0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
    1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0,
    0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
    0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
  ),
  byrow = TRUE, ncol = 12
)

multiplex_census(A, B)

Clique percolation

Description

Clique Percolation Method (CPM) is an algorithm for finding overlapping communities within networks, introduced by Palla et al. (2005). This function firstly identify cliques of size k, then creates a incidence matrix as an affiliation network.

Usage

percolation_clique(A)

Arguments

A

A matrix

Value

A matrix that assign each node to a clique

Author(s)

Alejandro Espinosa-Rada

References

Palla, G., Derényi, I., Farkas, I., & Vicsek, T. (2005). Uncovering the overlapping community structure of complex networks in nature and society. Nature, 435(7043), 814-818.

Examples

A <- matrix(
  c(
    0, 1, 1, 1, 0, 0, 0, 0, 0,
    1, 0, 1, 0, 0, 0, 0, 0, 0,
    1, 1, 0, 1, 0, 0, 0, 0, 0,
    1, 0, 1, 0, 1, 1, 0, 0, 0,
    0, 0, 0, 1, 0, 1, 1, 1, 0,
    0, 0, 0, 1, 1, 0, 1, 1, 0,
    0, 0, 0, 0, 1, 1, 0, 1, 1,
    0, 0, 0, 0, 1, 1, 1, 0, 0,
    0, 0, 0, 0, 0, 0, 1, 0, 0
  ),
  byrow = TRUE, ncol = 9
)
rownames(A) <- letters[1:nrow(A)]
colnames(A) <- letters[1:ncol(A)]
percolation_clique(A)

Permute labels of a matrix

Description

This function permutes the labels of a matrix.

Usage

perm_label(A, m = 1, unique = FALSE)

Arguments

A

A matrix
m

Number of permutations
unique

Whether to return unique cases

Value

This function returns the permutation of labels.

Author(s)

Alejandro Espinosa-Rada

Examples

W <- matrix(c(
  0, 1, 0, 0, 0,
  0, 0, 1, 0, 0,
  1, 0, 0, 0, 0,
  0, 0, 0, 0, 1,
  0, 0, 0, 1, 0
), byrow = TRUE, ncol = 5)
rownames(W) <- c("P", "Q", "R", "S", "T")
colnames(W) <- rownames(W)
perm_label(W, m = 1000, unique = TRUE)

Permutation matrix

Description

This function create permutation matrices.

Usage

perm_matrix(n, m = 1, unique = FALSE)

Arguments

n

The size of the square matri
m

Number of permutations
unique

Whether to return unique cases

Value

This function returns a list of permutation matrices

Author(s)

Alejandro Espinosa-Rada

Examples

W <- matrix(c(
  0, 1, 0, 0, 0,
  0, 0, 1, 0, 0,
  1, 0, 0, 0, 0,
  0, 0, 0, 0, 1,
  0, 0, 0, 1, 0
), byrow = TRUE, ncol = 5)
rownames(W) <- c("P", "Q", "R", "S", "T")
colnames(W) <- rownames(W)
perm_matrix(5, m = 1000, unique = TRUE)

Positive-negative centrality

Description

Positive-negative centrality

Usage

posneg_index(A, select = c("all", "in", "out"))

Arguments

A

A signed symmetric matrix (i.e., with ties that are either -1, 0 or 1)
select

Whether to consider the direction of the outgoing ties. Considering all (default), in or out ties.

Value

This function return the positive-negative centrality index for signed networks (Everett and Borgatti).

Source

Adapted from David Schoch 'signnet'

References

Everett, Martin and Borgatti, Stephen (2014). Networks containing negative ties. Social Networks, 38, 111-120. http://dx.doi.org/10.1016/j.socnet.2014.03.005

Examples

A <- matrix(
  c(
    0, 1, -1, -1, -1, -1, 0, 0, 0, 0, 0, -1, 0, 0, 1, 1,
    1, 0, -1, 0, -1, -1, 0, 0, -1, -1, 0, 0, 0, 0, 1, 1,
    -1, -1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0,
    -1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
    -1, -1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, -1, -1,
    -1, -1, 1, 0, 0, 0, 1, 1, -1, 0, 1, 1, -1, 0, 0, -1,
    0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0,
    0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, -1, 0, 0,
    0, -1, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 1, 0, -1, 0,
    0, -1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 1, 0, -1, 0,
    0, 0, 0, 0, 0, 1, 1, 1, -1, -1, 0, 1, -1, 0, -1, -1,
    -1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, -1, -1, -1,
    0, 0, 0, 0, 0, -1, 1, 0, 1, 1, -1, 0, 0, 1, -1, -1,
    0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, -1, 1, 0, 0, -1,
    1, 1, 0, 0, -1, 0, 0, 0, -1, -1, -1, -1, -1, 0, 0, 1,
    1, 1, 0, 0, -1, -1, 0, 0, 0, 0, -1, -1, -1, -1, 1, 0
  ),
  ncol = 16, nrow = 16, byrow = TRUE
)
label <- c(
  "Gavev", "Kotun", "Ove", "Alika", "Nagam", "Gahuk", "Masil", "Ukudz",
  "Notoh", "Kohik", "Geham", "Asaro", "Uheto", "Seuve", "Nagad", "Gama"
)
rownames(A) <- label
colnames(A) <- rownames(A)
posneg_index(A, select = c("all"))

Power matrix

Description

Power of a matrix computed by successive matrix multiplication.

Usage

power_function(A, n)

Arguments

A

A matrix
n

Positive integer

Value

This function return the power of a matrix by repeating matrix multiplication.

Author(s)

Alejandro Espinosa-Rada

References

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

Examples

A <- matrix(c(
  1, 0, 0, 0,
  1, 1, 0, 0,
  1, 0, 1, 0,
  0, 1, 1, 1
), byrow = TRUE, ncol = 4, nrow = 4)
power_function(A, 1000)

Q-analysis

Description

Q-structure of a simplicial complex.

Usage

q_analysis(A, simplicial_complex = FALSE, dimensions = FALSE)

Arguments

A

An incidence matrix
simplicial_complex

Whether the incidence matrix is a simplices or simplicial complexes representation
dimensions

Return the successively chains from high to low dimensions ($q$) and the number of components ($Q_p$)

Value

This function return a q-analysis of a simplicial complex matrix

Author(s)

Alejandro Espinosa-Rada

References

Atkin, R. H. (1974). Mathematical structure in human affairs. New York: Crane, Rusak.

Freeman, L. C. (1980). Q-analysis and the structure of friendship networks. International Journal of Man-Machine Studies, 12(4), 367–378. https://doi.org/10.1016/S0020-7373(80)80021-6

Examples

A <- matrix(c(
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0,
  0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
  0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
  0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
  0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0
), byrow = TRUE, ncol = 19)
colnames(A) <- letters[1:ncol(A)]
rownames(A) <- 1:nrow(A)

q_analysis(A, simplicial_complex = TRUE)

Reciprocity

Description

This measure calculated the reciprocity of an asymmetric matrix (directed graph).

Usage

recip_coef(
  A,
  diag = NULL,
  method = c("total_ratio", "ratio_nonnull", "global")
)

Arguments

A

A matrix
diag

Whether to consider the diagonal of the matrix
method

Whether to use total_ratio, ratio_nonnull or global reciprocity

Value

Return a reciprocity coefficient

Author(s)

Alejandro Espinosa-Rada A <- matrix(c(0,1,1,0, 1,0,1,0, 0,0,0,0, 1,0,0,0), byrow = TRUE, ncol = 4) recip_coef(A)

References

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

Redundancy measures

Description

Redundancy measures of the structural holes theory for binary matrixes

Usage

redundancy(A, ego = NULL, digraph = FALSE, weighted = FALSE)

Arguments

A

A symmetric matrix object
ego

Name of ego in the matrix
digraph

Whether the matrix is directed or undirected
weighted

Whether the matrix is weighted or not

Value

This function returns redundancy, effective size and efficincy measures (Burt, 1992).

Author(s)

Alejandro Espinosa-Rada

References

Burt, R.S., 1992. Structural Holes: the Social Structure of Competition. Harvard University Press, Cambridge.

Borgatti, S., 1997. Unpacking Burt's redundancy measure. Connections, 20(1): 35-38. doi: http://www.analytictech.com/connections/v20(1)/holes.htm

Examples

A <- matrix(c(
  0, 1, 0, 0, 1, 1, 1,
  1, 0, 0, 1, 0, 0, 1,
  0, 0, 0, 0, 0, 0, 1,
  0, 1, 0, 0, 0, 0, 1,
  1, 0, 0, 0, 0, 0, 1,
  1, 0, 0, 0, 0, 0, 1,
  1, 1, 1, 1, 1, 1, 0
), ncol = 7, byrow = TRUE)
rownames(A) <- letters[1:nrow(A)]
colnames(A) <- letters[1:ncol(A)]
redundancy(A, ego = "g")

Shared partners

Description

Shared partners

Usage

shared_partners(
  A,
  loops = FALSE,
  directed = TRUE,
  type = c("dsp", "esp", "nsp")
)

Arguments

A

A binary matrix
loops

Whether to consider the loops
directed

Whether the matrix is directed
type

Whether to return the dyad-wise (dsp) (default), edge-wise (esp) or non-edgewise (nsp) shared partners (Hunter and Handcock, 2006)

Value

This function return the distribution of shared partners.

Author(s)

Alejandro Espinosa-Rada

References

Hunter, D. R. and M. S. Handcock (2006), Inference in curved exponential family models for networks, Journal of Computational and Graphical Statistics, 15: 565– 583.

Examples

A <- matrix(c(
  0, 1, 0, 0, 0, 0,
  1, 0, 1, 1, 0, 1,
  0, 1, 0, 1, 0, 0,
  0, 1, 1, 0, 1, 1,
  0, 0, 0, 1, 0, 1,
  0, 1, 0, 1, 1, 0
), byrow = TRUE, ncol = 6)
shared_partners(A, type = "dsp")
shared_partners(A, type = "esp")
shared_partners(A, type = "nsp")

Simplicial complexes

Description

incidence matrix of simplexes or cliques

Usage

simplicial_complexes(A, zero_simplex = FALSE, projection = FALSE)

Arguments

A

A symmetric matrix object.
zero_simplex

Whether to include the zero simple.
projection

Whether to return the links between actors (i.e., rows) through their shared linking events (i.e., columns).

Value

This function return an incidence matrix of actors participating in simplices or simplicial complexes

Author(s)

Alejandro Espinosa-Rada

References

Atkin, R. H. (1974). Mathematical structure in human affairs. New York: Crane, Rusak.

Freeman, L. C. (1980). Q-analysis and the structure of friendship networks. International Journal of Man-Machine Studies, 12(4), 367–378. https://doi.org/10.1016/S0020-7373(80)80021-6

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

Examples

A <- matrix(c(
  0, 1, 1, 0, 0, 0, 0, 1, 0,
  1, 0, 1, 0, 0, 0, 0, 0, 0,
  1, 1, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 1, 1, 0, 0, 0,
  0, 0, 0, 1, 0, 0, 0, 0, 0,
  0, 0, 0, 1, 0, 0, 1, 1, 0,
  0, 0, 0, 0, 0, 1, 0, 1, 0,
  1, 0, 0, 0, 0, 1, 1, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0
), byrow = TRUE, ncol = 9)
rownames(A) <- letters[1:nrow(A)]
colnames(A) <- rownames(A)
simplicial_complexes(A, zero_simplex = FALSE)

Spatial autocorrelation

Description

This function calculate some spatial autocorrelations for a sample of networks at different orders (distances).

Usage

spatial_cor(
  A,
  V,
  measures = c("covariance", "correlation", "moran", "geary"),
  mean = TRUE,
  diag = FALSE,
  distance1 = TRUE,
  rowstand = FALSE,
  scale = FALSE
)

Arguments

A

A symmetric matrix
V

A vector
measures

Whether to use the Covariance covariance (default), Correlation correlation, Moran I moran or Geary's C geary
mean

Whether to use the mean of the vector for the measures
diag

Whether to consider the diagonal of the matrix for the measures
distance1

Whether to return only the spatial autocorrelation considering the actor at distance 1
rowstand

Whether to use the row-standardization to estimate Moran I (Anselin, 1995)
scale

Whether to scale Moran I (Anselin, 1995)

Value

This function return the global spatial autocorrelation. Multiple orders can also be computed.

References

Anselin, L. (1995). Local indicators of spatial association—LISA. Geographical analysis, 27(2), 93-115.

Geary, R.C. (1954). “The Contiguity Ratio and Statistical Mapping.” The Incorporated Statistician, 5: 115-145.

Moran, P.A.P. (1950). “Notes on Continuous Stochastic Phenomena.” Biometrika, 37: 17-23.

Examples

A <- matrix(c(
  0, 0, 1, 1,
  0, 0, 1, 0,
  1, 0, 0, 0,
  1, 0, 1, 0
), byrow = TRUE, ncol = 4)
V <- c(2, 2, 1, 1)

spatial_cor(A, V, measures = c("moran"))

Structural balance

Description

Structural balance

Usage

struc_balance(A, B = NULL, score = c("triangle", "walk"))

Arguments

A

A signed symmetric matrix (i.e., with ties that are either -1, 0 or 1)
B

A signed symmetric matrix considered as the negative ties (i.e., with ties that are either -1, 0 or 1)
score

Whether to return the triangle (default) or walk balance score (Aref and Wilson, 2017)

Value

This function return the structural balance (Heider, 1940; Cartwright and Harary, 1956). When B is used, matrix A is considered the negative matrix and A the positive matrix.

Author(s)

Alejandro Espinosa-Rada

References

Aref, Samin and Wilson, Mark C. (2017). Measuring partial balance in signed networks. Journal of Complex Networks, 6(4): 566-595.

Cartwright, Dorwin, and Harary, Frank (1956). Structural balance: a generalization of Heider's theory. Psychological review, 63(5), 277.

Heider, Fritz (1946). Attitudes and Cognitive Organization. The Journal of Psychology, 21: 107–112

Examples

A <- matrix(c(
  0, -1, -1, 0,
  -1, 0, 1, 0,
  -1, 1, 0, 0,
  0, 0, 0, 0
), byrow = TRUE, ncol = 4)
rownames(A) <- letters[1:nrow(A)]
colnames(A) <- rownames(A)
struc_balance(A)

Structural Missing Data

Description

Assign NA to missing data in matrices.

Usage

structural_na(
  A,
  label = NULL,
  row_labels = NULL,
  col_labels = NULL,
  two_mode = FALSE
)

Arguments

A

An incident or symmetric matrix object.
label

A string vector with the names of the theoretical complete matrix (used for one-mode networks only).
row_labels

A string vector with the names of the rows (used for two-mode networks).
col_labels

A string vector with the names of the columns (used for two-mode networks).
two_mode

Boolean indicating whether the matrix is two-mode. Default is FALSE.

Value

This function returns a matrix with NA assigned to missing data.

Examples

# Example for one-mode network
A <- matrix(c(
  0, 1, 1,
  1, 0, 1,
  0, 0, 0
), byrow = TRUE, ncol = 3)
colnames(A) <- c("A", "C", "D")
rownames(A) <- c("A", "C", "D")
label <- c("A", "B", "C", "D", "E")
structural_na(A, label = label)

# Example for two-mode network
B <- matrix(c(
  0, 1, 0,
  1, 0, 1,
  0, 1, 0,
  1, 0, 1
), byrow = TRUE, ncol = 3)
rownames(B) <- c("X1", "X2", "X3", "X4")
colnames(B) <- c("Y1", "Y2", "Y3")
rlabels <- c("X1", "X2", "X3", "X4", "X5")
clabels <- c("Y1", "Y2", "Y3", "Y4")
structural_na(B, row_labels = rlabels, col_labels = clabels, two_mode = TRUE)

Transitivity

Description

This measure is sometimes called clustering coefficient.

Usage

trans_coef(
  A,
  method = c("weakcensus", "global", "mean", "local"),
  select = c("all", "in", "out")
)

Arguments

A

A matrix
method

Whether to calculate the weakcensus, global transitivity ratio, the mean transitivity or the local transitivity.
select

Whether to consider all, in or out ties for the local transitivity.

Value

Return a transitivity measure

Author(s)

Alejandro Espinosa-Rada

References

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

Examples

A <- matrix(c(
  0, 1, 0, 1, 0,
  1, 0, 1, 1, 0,
  0, 1, 0, 0, 0,
  1, 1, 0, 0, 1,
  0, 0, 0, 1, 0
), byrow = TRUE, ncol = 5)
rownames(A) <- letters[1:ncol(A)]
colnames(A) <- rownames(A)

trans_coef(A, method = "local")

Transitivity matrix

Description

This function assigns a one in the elements of the matrix if a group of actors are part of a transitivity structure (030T label considering the MAN triad census)

Usage

trans_matrix(A, loops = FALSE)

Arguments

A

A matrix
loops

Whether to expect nonzero elements in the diagonal of the matrix

Value

A vector assigning an id the components that each of the nodes of the matrix belongs

Author(s)

Alejandro Espinosa-Rada

References

Davis, J.A. and Leinhardt, S. (1972). “The Structure of Positive Interpersonal Relations in Small Groups.” In J. Berger (Ed.), Sociological Theories in Progress, Vol. 2, 218-251. Boston: Houghton Mifflin.

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

Examples

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

Triad census analysis assuming U|MAN

Description

Considering the triad census of Davis and Leinhardt (1972) for vector A, B, and C:

Usage

triad_uman(A, ztest = FALSE, covar = FALSE)

Arguments

A

A symmetric matrix object
ztest

Return Z and p-value
covar

Return the covarianc matrix for triadic analysis

Details

003 = A,B,C, empty triad

012 = A -> B, C, triad with a single directed edge

102 = A <-> B, C, triad with a reciprocated connection between two vertices

021D = A <-B-> C, triadic out-star

021U = A -> B <- C triadic in-star

021C = A-> B-> C, directed line

111D = A <-> B <-C

111U = A <-> B-> C

030T = A-> B <-C, A-> C

030C = A <-B <-C, A-> C

201 = A <-> B <-> C

120D = A <-B-> C, A <-> C

120U = A-> B <-C, A <->C

120C = A-> B-> C, A <-> C

210 = A-> B <-> C, A <-> C

300 = A <-> B <-> C, A <->C, complete triad.

Value

This function gives the counts of the triad census, the expected counts, assuming that U|MAN distribution (Holland and Leinhardt, 1975, 1976) is operating, and the standard deviations of these counts.

Author(s)

Alejandro Espinosa-Rada

References

Davis, J.A. and Leinhardt, S. (1972). The Structure of Positive Interpersonal Relations in Small Groups. In J. Berger (Ed.), Sociological Theories in Progress, Volume 2, 218-251. Boston: Houghton Mifflin.

Holland, P. W. and Leinhardt, S. (1975). The statistical analysis of local structure in social networks. In D. R. Heise (Ed.), Sociological Methodology, 1976 (Jossey-Bass, pp. 1–45).

Holland, P. W. and Leinhardt, S. (1976). Local Structure in Social Networks. Sociological Methodology, 7, 1–45. doi: https://doi.org/10.2307/270703

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

Examples

data(krackhardt_friends)
triad_uman(krackhardt_friends)
## Not run: 
triad_uman(krackhardt_friends, ztest = TRUE, covar = TRUE)

## End(Not run)

Z test of the number of arcs

Description

Z test of the number of arcs

Usage

z_arctest(G, p = 0.5, interval = FALSE)

Arguments

G

A symmetric matrix object.
p

Constant probability p.
interval

Return a 95 percent confidence interval.

Value

This function gives a Z test and p-value for the number of lines or arcs present in a directed graph

Author(s)

Alejandro Espinosa-Rada

References

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

Examples

data(krackhardt_friends)
z_arctest(krackhardt_friends)

Zone-2 sampling from second-mode

Description

Second-zone multilevel sampling considering a second-mode focal actor

Usage

zone_sample(A, X, ego = TRUE, core = FALSE)

Arguments

A

A symmetric matrix object.
X

X an incidence matrix object.
ego

Whether to add or not ego into the subgraph.
core

Whether to add actors at distance one from ego

Value

This function return a list of second-zone subgraphs using as a focal actor the second-mode of the multilevel network.

Author(s)

Alejandro Espinosa-Rada

References

Espinosa-Rada, A. (2021). A Network Approach for the Sociological Study of Science: Modelling Dynamic Multilevel Networks. [PhD](https://research.manchester.ac.uk/en/studentTheses/a-network-approach-for-the-sociological-study-of-science-and-know). The University of Manchester.

Examples

A <- matrix(c(
  0, 1, 0, 0, 0, 0, 0, 0,
  0, 0, 1, 0, 0, 0, 0, 0,
  0, 1, 0, 1, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 1, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0
), byrow = TRUE, ncol = 8)
colnames(A) <- c("1", "2", "3", "4", "5", "6", "7", "8")
rownames(A) <- c("1", "2", "3", "4", "5", "6", "7", "8")

X <- matrix(c(
  1, 0, 0, 0,
  1, 0, 0, 0,
  1, 0, 1, 0,
  0, 1, 1, 0,
  0, 1, 1, 1,
  0, 1, 0, 0,
  0, 0, 0, 0,
  0, 0, 0, 1
), byrow = TRUE, ncol = 4)
colnames(X) <- c("a", "b", "c", "d")
rownames(X) <- c("1", "2", "3", "4", "5", "6", "7", "8")

set.seed(18051889)
zone_sample(A, X, core = TRUE)