README.md

In anespinosa/netmem: Social Network Measures using Matrices

netmem: Network Measures using Matrices

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

🖊 Author/mantainer: Alejandro Espinosa-Rada

🏫 Current: Institute of Sociology, Pontificia Universidad Católica de Chile

🏫 Before: 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.

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://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:

1. matrix_report(): Matrix report

2. matrix_adjlist(): Transform a matrix into an adjacency list

3. matrix_projection(): Unipartite projections

4. matrix_to_edgelist(): Transform a square matrix into an edge-list

5. adj_to_matrix(): Transform an adjacency list into a matrix

6. adj_to_incidence(): Transform an adjacency matrix into a incidence matrix

7. cumulativeSumMatrices(): Cumulative sum of matrices

8. edgelist_to_matrix(): Transform an edgelist into a matrix

9. expand_matrix(): Expand matrix

10. extract_component(): Extract components

11. hypergraph(): Hypergraphs

12. perm_matrix(): Permutation matrix

13. perm_label(): Permute labels of a matrix

14. power_function(): Power of a matrix

15. meta_matrix(): Meta matrix for multilevel networks

16. minmax_overlap(): Minimum/maximum overlap

17. mix_matrix(): Mixing matrix

18. simplicial_complexes(): Simplicial complexes

19. structural_na(): Structural missing data

20. ego_net(): Ego network

21. zone_sample(): Zone-2 sampling from second-mode

Ego and personal networks:

1. eb_constraint(): Constraint

2. ei_index(): Krackhardt and Stern’s E-I index

3. heterogeneity(): Blau’s and IQV index

4. redundancy(): Redundancy measures

Path distances:

1. bfs_ugraph(): Breath-first algorithm

2. compound_relation(): Relational composition

3. count_geodesics(): Count geodesic distances

4. short_path(): Shortest path

5. wlocal_distances(): Dijikstra’s algorithm (one actor)

6. wall_distances(): Dijikstra’s algorithm (all actors)

Signed networks:

1. posneg_index(): Positive-negative centrality

2. struc_balance(): Structural balance

Structural measures:

1. gen_density(): Generalized density

2. gen_degree(): Generalized degree

3. multilevel_degree(): Degree centrality for multilevel networks

4. recip_coef(): Reciprocity

5. trans_coef(): Transitivity

6. trans_matrix(): Transitivity matrix

7. components_id(): Components

8. k_core(): Generalized k-core

9. dyadic_census(): Dyad census

10. multiplex_census(): Multiplex triad census

11. mixed_census(): Multilevel triad and quadrilateral census

Cohesive subgroups:

1. clique_table(): Clique table

2. dyad_triad_table(): Forbidden triad table

3. percolation_clique(): Clique percolation

4. q_analysis(): Q-analysis

5. shared_partners(): Shared partners

Similarity measures:

1. bonacich_norm(): Bonacich normalization

2. co_ocurrence(): Co‐occurrence

3. dist_sim_matrix(): Structural similarities

4. fractional_approach(): Fractional approach

5. jaccard(): Jaccard similarity

Network inference:

1. kp_reciprocity(): Reciprocity of Katz and Powell

2. z_arctest(): Z test of the number of arcs

3. triad_uman(): Triad census analysis assuming U\|MAN

4. ind_rand_matrix(): Independent random matrix

Geographic information:

1. dist_geographic(): Geographical distances

2. spatial_cor(): Spatial autocorrelation

Data currently available:

1. FIFAego: Ego FIFA

2. FIFAex: Outside FIFA

3. FIFAin: Inside FIFA

4. krackhardt_friends: Krackhardt friends

5. 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:

### 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)

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"))

Other related R packages

• {bipartite}

• {migraph}

• {multinet}

• {muxViz}

• {tnet}

• {xUCINET}

anespinosa/netmem documentation built on April 5, 2025, 5:02 p.m.