The goal of netmem is to make
available different measures to analyse and manipulate complex networks
using matrices.
🖊 Author/mantainer: Alejandro Espinosa-Rada
🏫 Social Networks Lab ETH Zürich
The package implements different measures to analyse and manipulate complex multilayer networks, from an ego-centric perspective, considering one-mode networks, valued ties (i.e. weighted or multiplex) or with multiple levels.
To cite package ‘netmem’ in publications use:
Espinosa-Rada A (2023). netmem: Social Network Measures using Matrices. R package version 1.0-3, https://anespinosa.github.io/netmem/, https://github.com/anespinosa/netmem.
A BibTeX entry for LaTeX users is
@Manual{, title = {netmem: Social Network Measures using Matrices}, author = {Alejandro Espinosa-Rada}, year = {2023}, note = {R package version 1.0-3, https://anespinosa.github.io/netmem/}, url = {https://github.com/anespinosa/netmem}, }
Functions currently available in netmem:
Utilities:
-
matrix_report(): Matrix report -
matrix_adjlist(): Transform a matrix into an adjacency list -
matrix_projection(): Unipartite projections -
matrix_to_edgelist(): Transform a square matrix into an edge-list -
adj_to_matrix(): Transform an adjacency list into a matrix -
cumulativeSumMatrices(): Cumulative sum of matrices -
edgelist_to_matrix(): Transform an edgelist into a matrix -
expand_matrix(): Expand matrix -
extract_component(): Extract components -
hypergraph(): Hypergraphs -
perm_matrix(): Permutation matrix -
perm_label(): Permute labels of a matrix -
power_function(): Power of a matrix -
meta_matrix(): Meta matrix for multilevel networks -
minmax_overlap(): Minimum/maximum overlap -
mix_matrix(): Mixing matrix -
simplicial_complexes(): Simplicial complexes -
structural_na(): Structural missing data -
ego_net(): Ego network -
zone_sample(): Zone-2 sampling from second-mode
Ego and personal networks:
-
eb_constraint(): Constraint -
ei_index(): Krackhardt and Stern’s E-I index -
heterogeneity(): Blau’s and IQV index -
redundancy(): Redundancy measures
Path distances:
-
bfs_ugraph(): Breath-first algorithm -
compound_relation(): Relational composition -
count_geodesics(): Count geodesic distances -
short_path(): Shortest path -
wlocal_distances(): Dijikstra’s algorithm (one actor) -
wall_distances(): Dijikstra’s algorithm (all actors)
Signed networks:
-
posneg_index(): Positive-negative centrality -
struc_balance(): Structural balance
Structural measures:
-
gen_density(): Generalized density -
gen_degree(): Generalized degree -
multilevel_degree(): Degree centrality for multilevel networks -
recip_coef(): Reciprocity -
trans_coef(): Transitivity -
trans_matrix(): Transitivity matrix -
components_id(): Components -
k_core(): Generalized k-core -
dyadic_census(): Dyad census -
multiplex_census(): Multiplex triad census -
mixed_census(): Multilevel triad and quadrilateral census
Cohesive subgroups:
-
clique_table(): Clique table -
dyad_triad_table(): Forbidden triad table -
percolation_clique(): Clique percolation -
q_analysis(): Q-analysis -
shared_partners(): Shared partners
Similarity measures:
-
bonacich_norm(): Bonacich normalization -
co_ocurrence(): Co‐occurrence -
dist_sim_matrix(): Structural similarities -
fractional_approach(): Fractional approach -
jaccard(): Jaccard similarity
Network inference:
-
kp_reciprocity(): Reciprocity of Katz and Powell -
z_arctest(): Z test of the number of arcs -
triad_uman(): Triad census analysis assuming U|MAN -
ind_rand_matrix(): Independent random matrix
Geographic information:
-
dist_geographic(): Geographical distances -
spatial_cor(): Spatial autocorrelation
Data currently available:
-
FIFAego: Ego FIFA -
FIFAex: Outside FIFA -
FIFAin: Inside FIFA -
krackhardt_friends: Krackhardt friends -
lazega_lawfirm: Lazega Law Firm
Additional data in
classicnets: Classic Data of Social Networks
You can install the development version from GitHub with:
### OPTION 1
# install.packages("devtools")
devtools::install_github("anespinosa/netmem")
### OPTION 2
options(repos = c(
netmem = 'https://anespinosa.r-universe.dev',
CRAN = 'https://cloud.r-project.org'))
install.packages('netmem')library(netmem)Connections between individuals are often embedded in complex structures, which shape actors’ expectations, behaviours and outcomes over time. These structures can themselves be interdependent and exist at different levels. Multilevel networks are a means by which we can represent this complex system by using nodes and edges of different types. Check this book edited by Emmanuel Lazega and Tom A.B. Snijders or this book edited by David Knoke, Mario Diani, James Hollway and Dimitris Christopoulos.
For multilevel structures, we tend to collect the data in different matrices representing the variation of ties within and between levels. Often, we describe the connection between actors as an adjacency matrix and the relations between levels through incidence matrices. The comfortable combination of these matrices into a common structure would represent the multilevel network that could be highly complex.
Let’s assume that we have a multilevel network with two adjacency matrices, one valued matrix and two incidence matrices between them.
-
A1: Adjacency Matrix of the level 1 -
B1: incidence Matrix between level 1 and level 2 -
A2: Adjacency Matrix of the level 2 -
B2: incidence Matrix between level 2 and level 3 -
A3: Valued Matrix of the level 3
Create the data
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)We will start with a report of the matrices:
matrix_report(A1)
#> The matrix A might have the following characteristics:
#> --> The vectors of the matrix are `numeric`
#> --> No names assigned to the rows of the matrix
#> --> No names assigned to the columns of the matrix
#> --> Matrix is symmetric (network is undirected)
#> --> The matrix is square, 5 by 5
#> nodes edges
#> [1,] 5 7matrix_report(B1)
#> The matrix A might have the following characteristics:
#> --> The vectors of the matrix are `numeric`
#> --> No names assigned to the rows of the matrix
#> --> No names assigned to the columns of the matrix
#> --> The matrix is rectangular, 3 by 5
#> nodes_rows nodes_columns incidence_lines
#> [1,] 3 5 7matrix_report(A2)
#> The matrix A might have the following characteristics:
#> --> The vectors of the matrix are `numeric`
#> --> No names assigned to the rows of the matrix
#> --> No names assigned to the columns of the matrix
#> --> Matrix is symmetric (network is undirected)
#> --> The matrix is square, 3 by 3
#> nodes edges
#> [1,] 3 2matrix_report(B2)
#> The matrix A might have the following characteristics:
#> --> The vectors of the matrix are `numeric`
#> --> No names assigned to the rows of the matrix
#> --> No names assigned to the columns of the matrix
#> --> The matrix is rectangular, 4 by 3
#> nodes_rows nodes_columns incidence_lines
#> [1,] 4 3 5matrix_report(A3)
#> The matrix A might have the following characteristics:
#> --> The vectors of the matrix are `numeric`
#> --> No names assigned to the rows of the matrix
#> --> No names assigned to the columns of the matrix
#> --> Valued matrix
#> --> Matrix is symmetric (network is undirected)
#> --> The matrix is square, 4 by 4
#> nodes edges
#> [1,] 4 10What is the density of some of the matrices?
matrices <- list(A1, B1, A2, B2)
gen_density(matrices, multilayer = TRUE)
#> $`Density of matrix [[1]]`
#> [1] 0.7
#>
#> $`Density of matrix [[2]]`
#> [1] 0.4666667
#>
#> $`Density of matrix [[3]]`
#> [1] 0.6666667
#>
#> $`Density of matrix [[4]]`
#> [1] 0.4166667How about the degree centrality of the entire structure?
multilevel_degree(A1, B1, A2, B2, complete = TRUE)
#> multilevel bipartiteB1 bipartiteB2 tripartiteB1B2 low_multilevel
#> n1 3 1 NA 1 3
#> n2 5 2 NA 2 5
#> n3 3 1 NA 1 3
#> n4 4 1 NA 1 4
#> n5 6 2 NA 2 6
#> m1 6 2 2 4 4
#> m2 6 4 1 5 5
#> m3 4 1 2 3 3
#> k1 4 NA 1 1 1
#> k2 2 NA 1 1 1
#> k3 3 NA 2 2 2
#> k4 1 NA 1 1 1
#> meso_multilevel high_multilevel
#> n1 1 1
#> n2 2 2
#> n3 1 1
#> n4 1 1
#> n5 2 2
#> m1 6 4
#> m2 6 5
#> m3 4 3
#> k1 1 1
#> k2 1 1
#> k3 2 2
#> k4 1 1Besides, we can perform a k-core analysis of one of the levels using the information of an incidence matrix
k_core(A1, B1, multilevel = TRUE)
#> [1] 1 3 1 2 3This package also allows performing complex census for multilevel networks.
mixed_census(A2, t(B1), B2, quad = TRUE)
#> 000 100 001 010 020 200 11D0 11U0 120 210 220 002 01D1
#> 2 6 1 0 0 2 0 0 4 0 1 1 0
#> 01U1 012 021 022 101N 101P 201 102 202 11D1W 11U1P 11D1P 11U1W
#> 0 0 8 0 3 0 1 3 1 0 0 0 0
#> 121W 121P 21D1 21U1 11D2 11U2 221 122 212 222
#> 11 13 0 0 0 0 3 0 0 0When we are interested in one particular actor, we could perform
different network measures. For example, actor e has connections with
all the other actors in the network. Therefore, we could estimate some
of Ronald Burt’s measures.
# First we will assign names to the matrix
rownames(A1) <- letters[1:nrow(A1)]
colnames(A1) <- letters[1:ncol(A1)]
eb_constraint(A1, ego = "e")
#> $results
#> term1 term2 term3 constraint normalization
#> e 0.25 0.292 0.101 0.642 0.761
#>
#> $maximum
#> e
#> 0.766redundancy(A1, ego = "e")
#> $redundancy
#> [1] 1.5
#>
#> $effective_size
#> [1] 2.5
#>
#> $efficiency
#> [1] 0.625Also, sometimes we might want to subset a group of actors surrounding an ego.
ego_net(A1, ego = "e")
#> a b c d
#> a 0 1 0 0
#> b 1 0 0 1
#> c 0 0 0 1
#> d 0 1 1 0This package expand some measures for one-mode networks, such as the
generalized degree centrality. Suppose we consider a valued matrix A3.
If alpha=0 then it would only count the direct connections. But,
adding the tuning parameter alpha=0.5 would determine the relative
importance of the number of ties compared to tie weights.
gen_degree(A3, digraph = FALSE, weighted = TRUE)
#> [1] 3.872983 1.000000 4.000000 3.464102Also, we could conduct some exploratory analysis using the normalized degree of an incidence matrix.
gen_degree(B1, bipartite = TRUE, normalized = TRUE)
#> $bipartiteL1
#> [1] 0.3333333 0.6666667 0.3333333 0.3333333 0.6666667
#>
#> $bipartiteL2
#> [1] 0.4 0.8 0.2This package also implements some analysis of dyads.
# dyad census
dyadic_census(A1)
#> Mutual Asymmetrics Nulls
#> 7 0 3# Katz and Powell reciprocity
kp_reciprocity(A1)
#> [1] 6.333333# Z test of the number of arcs
z_arctest(A1)
#> z p
#> 1.789 0.074We can also check the triad census assuming conditional uniform distribution considering different types of dyads (U|MAN)
triad_uman(A1)
#> label OBS EXP VAR STD
#> 1 003 0 0.083 0.076 0.276
#> 2 012 0 0.000 0.000 0.000
#> 3 102 2 1.750 0.688 0.829
#> 4 021D 0 0.000 0.000 0.000
#> 5 021U 0 0.000 0.000 0.000
#> 6 021C 0 0.000 0.000 0.000
#> 7 111D 0 0.000 0.000 0.000
#> 8 111U 0 0.000 0.000 0.000
#> 9 030T 0 0.000 0.000 0.000
#> 10 030C 0 0.000 0.000 0.000
#> 11 201 5 5.250 1.688 1.299
#> 12 120D 0 0.000 0.000 0.000
#> 13 120U 0 0.000 0.000 0.000
#> 14 120C 0 0.000 0.000 0.000
#> 15 210 0 0.000 0.000 0.000
#> 16 300 3 2.917 0.410 0.640Please note that this project is released with a Contributor Code of Conduct. By participating in this project you agree to abide by its terms.
# library(todor)
# todor::todor_package(c("TODO", "FIXME"))