The goal of netmem is to make available different measures to analyse and manipulate complex networks using matrices.

🖊 Author/mantainer: Alejandro Espinosa-Rada

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.

Citation

To cite package ‘netmem’ in publications use:

Espinosa-Rada A (2023). netmem: Social Network Measures using Matrices. R package version 1.0-3, 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}, 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
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 normalisation
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

Quick overview of `netmem: Network Measures using Matrices`

Installation

You can install the development version from GitHub with:

# install.packages("devtools")
devtools::install_github("anespinosa/netmem")

library(netmem)

Multilevel Networks

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.

Example

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     7
matrix_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               7
matrix_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     2
matrix_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               5
matrix_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    10

What 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] 0.4166667

How 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               1

Besides, 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 3

This 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     0

Ego measures

When 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 
#> 0.766
redundancy(A1, ego = "e")
#> $redundancy
#> [1] 1.5
#> 
#> $effective_size
#> [1] 2.5
#> 
#> $efficiency
#> [1] 0.625

Also, 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 0

One-mode network

This 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 3.464102

Also, 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 0.2

This 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 0.074

We 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 0.640

Code of conduct

Please note that this project is released with a Contributor Code of Conduct. By participating in this project you agree to abide by its terms.

To-do list

# library(todor)
# todor::todor_package(c("TODO", "FIXME"))

netmem: Network Measures using Matrices