In anespinosa/netmem: Social Network Measures using Matrices

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netmem: Network Measures using Matrices

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

# Check if the 'devtools' package is installed
if (!requireNamespace("devtools", quietly = TRUE)) {
  install.packages("devtools")
}

# Check if the 'emo' package is installed via devtools
if (!requireNamespace("emo", quietly = TRUE)) {
  devtools::install_github("hadley/emo")
}

r emo::ji("pen") Author/mantainer: Alejandro Espinosa-Rada

r emo::ji("school") Current: Institute of Sociology, Pontificia Universidad Católica de Chile

r emo::ji("school") 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

citation(package = "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

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Quick overview of netmem: Network Measures using Matrices

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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)
matrix_report(B1)
matrix_report(A2)
matrix_report(B2)
matrix_report(A3)

What is the density of some of the matrices?

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

How about the degree centrality of the entire structure?

multilevel_degree(A1, B1, A2, B2, complete = TRUE)

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)

This package also allows performing complex census for multilevel networks.

mixed_census(A2, t(B1), B2, quad = TRUE)

---

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")
redundancy(A1, ego = "e")

Also, sometimes we might want to subset a group of actors surrounding an ego.

ego_net(A1, ego = "e")

---

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)

Also, we could conduct some exploratory analysis using the normalized degree of an incidence matrix.

gen_degree(B1, bipartite = TRUE, normalized = TRUE)

This package also implements some analysis of dyads.

# dyad census
dyadic_census(A1)

# Katz and Powell reciprocity
kp_reciprocity(A1)

# Z test of the number of arcs
z_arctest(A1)

We can also check the triad census assuming conditional uniform distribution considering different types of dyads (U|MAN)

triad_uman(A1)

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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.

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To-do list

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

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Other related R packages

• {bipartite}

• {migraph}

• {multinet}

• {muxViz}

• {tnet}

• {xUCINET}

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