| Title: | Methods to Analyse Signed Networks |
| Version: | 1.0.5 |
| Description: | Methods for the analysis of signed networks. This includes several measures for structural balance as introduced by Cartwright and Harary (1956) <doi:10.1037/h0046049>, blockmodeling algorithms from Doreian (2008) <doi:10.1016/j.socnet.2008.03.005>, various centrality indices, and projections of signed two-mode networks introduced by Schoch (2020) <doi:10.1080/0022250X.2019.1711376>. |
| License: | MIT + file LICENSE |
| URL: | https://github.com/schochastics/signnet, https://schochastics.github.io/signnet/ |
| BugReports: | https://github.com/schochastics/signnet/issues |
| Depends: | R (≥ 3.2.0) |
| Imports: | igraph, Matrix, Rcpp |
| Suggests: | covr, ggplot2, ggraph, knitr, ompr, ompr.roi, rmarkdown, ROI, ROI.plugin.glpk, testthat (≥ 2.1.0) |
| LinkingTo: | Rcpp, RcppArmadillo |
| VignetteBuilder: | knitr |
| Encoding: | UTF-8 |
| LazyData: | true |
| RoxygenNote: | 7.3.2 |
| NeedsCompilation: | yes |
| Packaged: | 2025-02-05 19:38:20 UTC; david |
| Author: | David Schoch 
[aut, cre] |
| Maintainer: | David Schoch <david@schochastics.net> |
| Repository: | CRAN |
| Date/Publication: | 2025-02-05 20:40:02 UTC |
Convert a signed graph to a complex adjacency matrix
Description
This function returns the adjacency matrix for a signed graph that contains ambivalent ties
Usage
as_adj_complex(g, attr)
Arguments
g |
igraph object |
attr |
edge attribute name that encodes positive ("P"), negative ("N") and ambivalent ("A") ties. |
Value
complex adjacency matrix
See Also
Convert a signed graph to a signed adjacency matrix
Description
This function returns the adjacency matrix for a signed graph
Usage
as_adj_signed(g, sparse = FALSE)
Arguments
g |
igraph object. Must have a "sign" edge attribute. |
sparse |
Logical scalar, whether to return the result as a sparse matrix. The Matrix package is required for sparse matrices. |
Value
signed adjacency matrix
See Also
Convert Signed Network to Complex
Description
Convert Signed Network to Complex
Usage
as_complex_edges(g, attr = "type")
Arguments
g |
igraph object. Must have a "sign" edge attribute. |
attr |
new edge attribute name that encodes positive ("P"), negative ("N") and ambivalent ("A") ties. |
Value
igraph object
Author(s)
David Schoch
Examples
g <- sample_islands_signed(2, 10, 1, 10)
as_complex_edges(g)
Complex Incidence Matrix
Description
The complex incidence matrix of a signed graph containing ambivalent ties.
Usage
as_incidence_complex(g, attr)
Arguments
g |
igraph object. |
attr |
edge attribute name that encodes positive ("P"), negative ("N") and ambivalent ("A") ties. |
Details
This function is slightly different than as_incidence_matrix since it is defined for bipartite graphs.
The incidence matrix here is defined as a S \in C^{n,m}, where n is the number of vertices and m the number of edges. Edges (i,j) are oriented such that i<j and entries are defined as
S_{i(i,j)}=\sqrt{A_{ij}}
S_{j(i,j)}=-\sqrt{A_{ji}} if (i,j) is an ambivalent tie
S_{j(i,j)}=-A_{ji}\sqrt{A_{ji}} else
Value
a complex matrix
Author(s)
David Schoch
See Also
laplacian_matrix_complex,as_adj_complex
Convert a signed two-mode network to a signed matrix
Description
This function returns the incidence matrix for a signed two-mode network.
Usage
as_incidence_signed(g, sparse = FALSE)
Arguments
g |
igraph object (bipartite). Must have a "sign" edge attribute. |
sparse |
Logical scalar, whether to return the result as a sparse matrix. The Matrix package is required for sparse matrices. |
Value
signed incidence matrix
convert unsigned projection to signed
Description
convert unsigned projection to signed
Usage
as_signed_proj(g)
Arguments
g |
igraph object |
Value
igraph object
Author(s)
David Schoch
See Also
Examples
library(igraph)
# create a simple signed two mode network
el <- matrix(c(1, "a", 1, "b", 1, "c", 2, "a", 2, "b"), ncol = 2, byrow = TRUE)
g <- graph_from_edgelist(el, directed = FALSE)
E(g)$sign <- c(1, 1, -1, 1, -1)
V(g)$type <- c(FALSE, TRUE, TRUE, TRUE, FALSE)
# convert to unsigned two-mode network and project
l <- as_unsigned_2mode(g, primary = TRUE)
p <- bipartite_projection(l, which = "true")
# turn the unsigned projection back to a signed network
as_signed_proj(p)
convert signed two-mode network to unsigned
Description
convert signed two-mode network to unsigned
Usage
as_unsigned_2mode(g, primary = TRUE)
Arguments
g |
igraph object. Two-mode network, must have a "sign" edge attribute. |
primary |
logical. Which mode to transform |
Value
igraph object
Author(s)
David Schoch
See Also
Examples
library(igraph)
# create a simple signed two mode network
el <- matrix(c(1, "a", 1, "b", 1, "c", 2, "a", 2, "b"), ncol = 2, byrow = TRUE)
g <- graph_from_edgelist(el, directed = FALSE)
E(g)$sign <- c(1, 1, -1, 1, -1)
V(g)$type <- c(FALSE, TRUE, TRUE, TRUE, FALSE)
# convert to unsigned two-mode network and project
l <- as_unsigned_2mode(g, primary = TRUE)
p <- bipartite_projection(l, which = "true")
# turn the unsigned projection back to a signed network
as_signed_proj(p)
Signed networks from Avatar: The Last Airbender
Description
Allies/Enemy relations from Avatar: The Last Airbender
Usage
avatar
Format
igraph object
Source
scraped from Avatar Wiki (https://avatar.fandom.com/wiki/Category:Characters)
balancedness of signed network
Description
Implements several indices to assess the balancedness of a network.
Usage
balance_score(g, method = "triangles")
Arguments
g |
igraph object with a sign edge attribute. |
method |
string indicating the method to be used. See details for options |
Details
The method parameter can be one of
- triangles
Fraction of balanced triangles. Maximal (=1) if all triangles are balanced.
- walk
\sum exp(\lambda_i) / \sum exp(\mu_i)
where \lambda_i are the eigenvalues of the
signed adjacency matrix and \mu_i of the unsigned adjacency matrix. Maximal (=1) if all walks are balanced.
- frustration
The frustration index assumes that the network can be partitioned into two groups, where intra group edges are positive and inter group edges are negative. The index is defined as the sum of intra group negative and inter group positive edges. Note that the problem is NP complete and only an upper bound is returned (based on simulated annealing). Exact methods can be found in the work of Aref. The index is normalized such that it is maximal (=1) if the network is balanced.
Value
numeric balancedness score between 0 and 1
Author(s)
David Schoch
References
Estrada, E. (2019). Rethinking structural balance in signed social networks. Discrete Applied Mathematics.
Samin Aref, Mark C Wilson (2018). Measuring partial balance in signed networks. Journal of Complex Networks, 6(4): 566–595, https://doi.org/10.1093/comnet/cnx044
Examples
library(igraph)
g <- graph.full(4)
E(g)$sign <- c(-1, 1, 1, -1, -1, 1)
balance_score(g, method = "triangles")
balance_score(g, method = "walk")
Count Walks in complex signed network
Description
Count Walks in complex signed network
Usage
complex_walks(g, attr, k)
Arguments
g |
igraph object. |
attr |
edge attribute that encodes positive ("P"), negative ("N") and ambivalent ("A") ties. |
k |
integer. length of walks |
Value
igraph object
Author(s)
David Schoch
Examples
g <- sample_islands_signed(2, 10, 1, 10)
g <- as_complex_edges(g, attr = "type")
complex_walks(g, attr = "type", k = 3)
count complex triangles
Description
Counts the number of all possible signed triangles (+++),(++-), (+–) and (—)
Usage
count_complex_triangles(g, attr)
Arguments
g |
igraph object. |
attr |
edge attribute name that encodes positive ("P"), negative ("N") and ambivalent ("A") ties. |
Value
counts for all complex triangle types
Author(s)
David Schoch
See Also
Examples
library(igraph)
g <- make_full_graph(4)
E(g)$type <- c("P", "N", "A", "A", "P", "N")
count_complex_triangles(g, attr = "type")
count signed triangles
Description
Counts the number of all possible signed triangles (+++),(++-), (+–) and (—)
Usage
count_signed_triangles(g)
Arguments
g |
igraph object with a sign edge attribute. |
Value
counts for all 4 signed triangle types
Author(s)
David Schoch
See Also
Examples
library(igraph)
g <- make_full_graph(4)
E(g)$sign <- c(-1, 1, 1, -1, -1, 1)
count_signed_triangles(g)
Signed networks from Correlates of War
Description
51 signed networks of inter state relations
Usage
cowList
Format
List of igraph objects
Source
http://mrvar.fdv.uni-lj.si/pajek/SVG/CoW/default.htm
References
Doreian, P. and Mrvar, A. (2015). "Structural Balance and Signed International Relations". Journal of Social Structure, 16(2)
Signed Degree
Description
several options to calculate the signed degree of vertices
Usage
degree_signed(
g,
mode = c("all", "in", "out"),
type = c("pos", "neg", "ratio", "net")
)
Arguments
g |
igraph object with a sign edge attribute. |
mode |
character string, “out” for out-degree, “in” for in-degree or “all” for undirected networks. |
type |
character string, “pos” or “neg” for counting positive or negative neighbors only, "ratio" for pos/(pos+neg), or "net" for pos-neg. |
Value
centrality scores as numeric vector.
Author(s)
David Schoch
Signed Eigenvector centrality
Description
returns the eigenvector associated with the dominant eigenvalue from the adjacency matrix.
Usage
eigen_centrality_signed(g, scale = TRUE)
Arguments
g |
igraph object with a sign edge attribute. |
scale |
Logical scalar, whether to scale the result to have a maximum score of one. If no scaling is used then the result vector is the same as returned by |
Details
Note that, with negative values, the adjacency matrix may not have a dominant eigenvalue. This means it is not clear which eigenvector should be used. In addition it is possible for the adjacency matrix to have repeated eigenvalues and hence multiple linearly independent eigenvectors. In this case certain centralities can be arbitrarily assigned. The function returns an error if this is the case.
Value
centrality scores as numeric vector.
Author(s)
David Schoch
References
Bonacich, P. and Lloyd, P. (2004). "Calculating Status with Negative Relations." Social Networks 26 (4): 331–38.
Everett, M. and Borgatti, S.P. (2014). "Networks Containing Negative Ties." Social Networks 38: 111–20.
Examples
library(igraph)
data("tribes")
eigen_centrality_signed(tribes)
Exact frustration index of a signed network
Description
Computes the exact frustration index of a signed network using linear programming
Usage
frustration_exact(g, ...)
Arguments
g |
signed network |
... |
additional parameters for the ompr solver |
Details
The frustration index indicates the minimum number of edges whose removal results in a balance
network. The function needs the following packages to be installed: ompr, ompr.roi,ROI, and ROI.plugin.glpk.
The function Implements the AND model in Aref et al., 2020
Value
list containing the frustration index and the bipartition of nodes
Author(s)
David Schoch
References
Aref, Samin, Andrew J. Mason, and Mark C. Wilson. "Computing the line index of balance using linear programming optimisation." Optimization problems in graph theory. Springer, Cham, 2018. 65-84.
Aref, Samin, Andrew J. Mason, and Mark C. Wilson. "A modeling and computational study of the frustration index in signed networks." Networks 75.1 (2020): 95-110.
Plot Blockmodel matrix
Description
Plot Blockmodel matrix
Usage
ggblock(
g,
blocks = NULL,
cols = NULL,
show_blocks = FALSE,
show_labels = FALSE
)
Arguments
g |
igraph object with a sign edge attribute. |
blocks |
vector of block membership as obtained, e.g. from signed_blockmodel |
cols |
colors used for negative and positive ties |
show_blocks |
logical. Should block borders be displayed? (Default: FALSE) |
show_labels |
logical. Should node labels be displayed? (Default: FALSE) |
Value
ggplot2 object
Author(s)
David Schoch
Examples
## Not run:
library(igraph)
data("tribes")
clu <- signed_blockmodel(tribes, k = 3, alpha = 0.5, annealing = TRUE)
ggblock(tribes, clu$membership, show_blocks = TRUE, show_labels = TRUE)
## End(Not run)
Plot a signed or complex network
Description
Plot a signed or complex network
Usage
ggsigned(g, type = "signed", attr = NULL, edge_cols = NULL, weights = FALSE)
Arguments
g |
igraph object. Must have a "sign" edge attribute or an attribute containing "P", "N", "A" |
type |
character string. either "signed" or "complex" |
attr |
character string. edge attribute that containing "P", "N", "A" if type="complex" |
edge_cols |
colors used for negative and positive (and ambivalent) ties |
weights |
logical. If TRUE, weights are computed based on sign. Defaults to FALSE |
Details
This is a very rudimentary visualization of a signed network. If you are fluent in 'ggraph', you can probably cook up something more sophisticated. The function is thus mostly meant to give a quick overview of the network.
Value
ggplot2 object
Author(s)
David Schoch
circular signed graph
Description
circular graph with positive and negative edges.
Usage
graph_circular_signed(n, r = 1, pos = 0.1, neg = 0.1)
Arguments
n |
number of nodes |
r |
radius |
pos |
distance fraction between positive edges |
neg |
distance fraction between negative edges |
Value
igraph graph
Author(s)
David Schoch
Examples
library(igraph)
graph_circular_signed(n = 50)
Create signed graphs from adjacency matrices
Description
Create signed graphs from adjacency matrices
Usage
graph_from_adjacency_matrix_signed(A, mode = "undirected", ...)
Arguments
A |
square adjacency matrix of a signed graph |
mode |
Character scalar, specifies how to interpret the supplied matrix. Possible values are: directed, undirected |
... |
additional parameters for |
Value
a signed network as igraph object
Examples
A <- matrix(c(0, 1, -1, 1, 0, 1, -1, 1, 0), 3, 3)
graph_from_adjacency_matrix_signed(A)
Create a signed graph from an edgelist matrix
Description
Create a signed graph from an edgelist matrix
Usage
graph_from_edgelist_signed(el, signs, directed = FALSE)
Arguments
el |
The edgelist, a two column matrix, character or numeric. |
signs |
vector indicating the sign of edges. Entries must be 1 or -1. |
directed |
whether to create a directed graph. |
Value
a signed network as igraph object
Examples
el <- matrix(c("foo", "bar", "bar", "foobar"), ncol = 2, byrow = TRUE)
signs <- c(-1, 1)
graph_from_edgelist_signed(el, signs)
Check if network is a signed network
Description
Check if network is a signed network
Usage
is_signed(g)
Arguments
g |
igraph object |
Value
logical scalar
Examples
g <- sample_islands_signed(2, 5, 1, 5)
is_signed(g)
Complex Graph Laplacian
Description
The Laplacian of a signed graph containing ambivalent ties.
Usage
laplacian_matrix_complex(g, attr, norm = FALSE)
Arguments
g |
igraph object. |
attr |
edge attribute name that encodes positive ("P"), negative ("N") and ambivalent ("A") ties. |
norm |
Whether to calculate the normalized Laplacian. See definitions below. |
Details
See laplacian_matrix of igraph for more details. In the complex case, D is a diagonal matrix containing the absolute values of row sums of the complex adjacency matrix.
Value
a complex matrix
Author(s)
David Schoch
See Also
Signed Graph Laplacian
Description
The Laplacian of a signed graph.
Usage
laplacian_matrix_signed(g, norm = FALSE, sparse = FALSE)
Arguments
g |
igraph object with a sign edge attribute. |
norm |
Whether to calculate the normalized Laplacian. See definitions below. |
sparse |
Logical scalar, whether to return the result as a sparse matrix. The Matrix package is required for sparse matrices. |
Details
See laplacian_matrix of igraph for more details. In the signed case, D is a diagonal matrix containing the absolute values of row sums of the signed adjacency matrix.
Value
a numeric matrix
Author(s)
David Schoch
Examples
library(igraph)
g <- sample_islands_signed(3, 10, 5 / 10, 1)
laplacian_matrix_signed(g)
laplacian_matrix_signed(g, norm = TRUE)
PN Centrality Index
Description
centrality index for signed networks by Everett and Borgatti
Usage
pn_index(g, mode = c("all", "in", "out"))
Arguments
g |
igraph object with a sign edge attribute. |
mode |
character string, “out” for out-pn, “in” for in-pn or “all” for undirected networks. |
Value
centrality scores as numeric vector.
Author(s)
David Schoch
References
Everett, M. and Borgatti, S. (2014) Networks containing negative ties. Social Networks 38 111-120
Examples
A <- matrix(c(
0, 1, 0, 1, 0, 0, 0, -1, -1, 0,
1, 0, 1, -1, 1, -1, -1, 0, 0, 0,
0, 1, 0, 1, -1, 0, 0, 0, -1, 0,
1, -1, 1, 0, 1, -1, -1, 0, 0, 0,
0, 1, -1, 1, 0, 1, 0, -1, 0, -1,
0, -1, 0, -1, 1, 0, 1, 0, 1, -1,
0, -1, 0, -1, 0, 1, 0, 1, -1, 1,
-1, 0, 0, 0, -1, 0, 1, 0, 1, 0,
-1, 0, -1, 0, 0, 1, -1, 1, 0, 1,
0, 0, 0, 0, -1, -1, 1, 0, 1, 0
), 10, 10)
g <- graph_from_adjacency_matrix_signed(A,"undirected")
pn_index(g)
Bipartite random signed graphs
Description
Bipartite random signed graphs
Usage
sample_bipartite_signed(
n1,
n2,
p,
p_neg,
directed = FALSE,
mode = c("out", "in", "all")
)
Arguments
n1 |
Integer scalar, the number of bottom vertices. |
n2 |
Integer scalar, the number of top vertices. |
p |
The probability for drawing an edge between two arbitrary vertices. |
p_neg |
The probability of a drawn edge to be a negative tie |
directed |
logical, whether the graph will be directed. defaults to FALSE. |
mode |
Character scalar, specifies how to direct the edges in directed graphs. If it is ‘out’, then directed edges point from bottom vertices to top vertices. If it is ‘in’, edges point from top vertices to bottom vertices. ‘out’ and ‘in’ do not generate mutual edges. If this argument is ‘all’, then each edge direction is considered independently and mutual edges might be generated. This argument is ignored for undirected graphs. |
Value
A signed bipartite igraph graph.
Examples
sample_bipartite_signed(10, 10, 0.5, 0.5)
Generate random signed graphs according to the G(n,p) Erdos-Renyi model
Description
Generate random signed graphs according to the G(n,p) Erdos-Renyi model
Usage
sample_gnp_signed(n, p, p_neg, directed = FALSE, loops = FALSE)
Arguments
n |
The number of vertices in the graph. |
p |
The probability for drawing an edge between two arbitrary vertices. |
p_neg |
The probability of a drawn edge to be a negative tie |
directed |
logical, whether the graph will be directed. defaults to FALSE. |
loops |
logical, whether to add loop edges, defaults to FALSE. |
Value
a signed igraph graph object
References
Erdos, P. and Renyi, A., On random graphs, Publicationes Mathematicae 6, 290–297 (1959).
Examples
sample_gnp_signed(10, 0.4, 0.5)
A graph with random subgraphs connected by negative edges
Description
Create a number of Erdos-Renyi random graphs with identical parameters, and connect them with the specified number of negative ties.
Usage
sample_islands_signed(islands.n, islands.size, islands.pin, n.inter)
Arguments
islands.n |
The number of islands in the graph. |
islands.size |
The size of the islands in the graph. |
islands.pin |
The probability of intra-island edges. |
n.inter |
number of negative edges between two islands. |
Value
a signed igraph graph
Author(s)
David Schoch
Examples
library(igraph)
sample_islands_signed(3, 10, 0.5, 1)
Blockmodeling for signed networks
Description
Finds blocks of nodes with intra-positive and inter-negative edges
Usage
signed_blockmodel(g, k, alpha = 0.5, annealing = FALSE)
Arguments
g |
igraph object with a sign edge attribute. |
k |
number of blocks |
alpha |
see details |
annealing |
logical. if TRUE, use simulated annealing (Default: FALSE) |
Details
The function minimizes P(C)=\alphaN+(1-\alpha)P,
where N is the total number of negative ties within plus-sets and P be the total number of
positive ties between plus-sets. This function implements the structural balance model. That is,
all diagonal blocks are positive and off-diagonal blocks negative.
For the generalized version see signed_blockmodel_general.
Value
numeric vector of block assignments and the associated criterion value
Author(s)
David Schoch
References
Doreian, Patrick and Andrej Mrvar (2009). Partitioning signed social networks. Social Networks 31(1) 1-11
Examples
library(igraph)
g <- sample_islands_signed(10, 10, 1, 20)
clu <- signed_blockmodel(g, k = 10, alpha = 0.5)
table(clu$membership)
clu$criterion
# Using simulated annealing (less change of getting trapped in local optima)
data("tribes")
clu <- signed_blockmodel(tribes, k = 3, alpha = 0.5, annealing = TRUE)
table(clu$membership)
clu$criterion
Generalized blockmodeling for signed networks
Description
Finds blocks of nodes with specified inter/intra group ties
Usage
signed_blockmodel_general(g, blockmat, alpha = 0.5)
Arguments
g |
igraph object with a sign edge attribute. |
blockmat |
Integer Matrix. Specifies the inter/intra group patterns of ties |
alpha |
see details |
Details
The function minimizes P(C)=\alphaN+(1-\alpha)P,
where N is the total number of negative ties within plus-sets and P be the total number of
positive ties between plus-sets. This function implements the generalized model. For the structural balance
version see signed_blockmodel.
Value
numeric vector of block assignments and the associated criterion value
Author(s)
David Schoch
References
Doreian, Patrick and Andrej Mrvar (2009). Partitioning signed social networks. Social Networks 31(1) 1-11
Examples
library(igraph)
# create a signed network with three groups and different inter/intra group ties
g1 <- g2 <- g3 <- make_full_graph(5)
V(g1)$name <- as.character(1:5)
V(g2)$name <- as.character(6:10)
V(g3)$name <- as.character(11:15)
g <- Reduce("%u%", list(g1, g2, g3))
E(g)$sign <- 1
E(g)$sign[1:10] <- -1
g <- add_edges(g, c(rbind(1:5, 6:10)), attr = list(sign = -1))
g <- add_edges(g, c(rbind(1:5, 11:15)), attr = list(sign = -1))
g <- add_edges(g, c(rbind(11:15, 6:10)), attr = list(sign = 1))
# specify the link patterns between groups
blockmat <- matrix(c(1, -1, -1, -1, 1, 1, -1, 1, -1), 3, 3, byrow = TRUE)
signed_blockmodel_general(g, blockmat, 0.5)
list signed triangles
Description
lists all possible signed triangles
Usage
signed_triangles(g)
Arguments
g |
igraph object with a sign edge attribute. |
Value
matrix of vertex ids and the number of positive ties per triangle
Author(s)
David Schoch
See Also
Examples
library(igraph)
g <- make_full_graph(4)
E(g)$sign <- c(-1, 1, 1, -1, -1, 1)
signed_triangles(g)
signed triad census
Description
triad census for signed graphs
Usage
triad_census_signed(g)
Arguments
g |
igraph object with a sign edge attribute. |
Value
counts for all 139 signed directed triangle types
Author(s)
David Schoch
Examples
library(igraph)
g <- make_full_graph(4, directed = TRUE)
E(g)$sign <- rep(c(-1, 1, 1, -1, -1, 1), 2)
triad_census_signed(g)
Signed network of New Guinean highland tribes
Description
Signed social network of tribes of the Gahuku–Gama alliance structure of the Eastern Central Highlands of New Guinea, from Kenneth Read. The network contains sixteen tribes connected by friendship ("rova") and enmity ("hina").
Usage
tribes
Format
An igraph object
Source
http://vlado.fmf.uni-lj.si/pub/networks/data/ucinet/gama.dat
References
Read, K. E. (1954) Cultures of the central highlands, New Guinea. Southwestern Journal of Anthropology, 1–43.