wdnet: Weighted and Directed Networks

Description

This package provides functions to conduct network analysis

• Assortativity, centrality, clustering coefficient for weighted and directed networks

• Rewire an unweighted network with given assortativity coefficient(s)

• Preferential attachment (PA) network generation

wdnet networks

wdnet networks have a class wdnet. It is a list containing the following components:

• A logical value directed indicating if the network is directed.

• A logical value weighted indicating if the network is weighted.

• A two-column matrix edgelist representing the edges.

• A data frame node.attr that includes node attributes, such as node strengths.

• A data frame edge.attr that includes edge attributes, such as edge weights.

Creating a wdnet Object

• To generate a preferential attachment (PA) network, use rpanet().

• To create a wdnet object from an edge list and edge weights, use edgelist_to_wdnet().

• To create a wdnet object from an adjacency matrix, use adj_to_wdnet().

• To convert an igraph object to a wdnet object, use igraph_to_wdnet().

Further information

The development version of this package is available on Gitlab (https://gitlab.com/wdnetwork/wdnet).

Author(s)

Maintainer: Yelie Yuan yelie.yuan@uconn.edu

Authors:

• Tiandong Wang td_wang@fudan.edu.cn

• Jun Yan jun.yan@uconn.edu

• Panpan Zhang panpan.zhang@vumc.org

See Also

Useful links:

• https://gitlab.com/wdnetwork/wdnet

• Report bugs at https://gitlab.com/wdnetwork/wdnet/-/issues

Add components to the control list

Description

'+' is used to combine components to control the PA network generation process. Available components are rpa_control_scenario(), rpa_control_edgeweight(), rpa_control_newedge(), rpa_control_preference() and rpa_control_reciprocal().

Usage

## S3 method for class 'rpacontrol'
e1 + e2

Arguments

Value

A list of class rpacontrol with components from e1 and e2.

Examples

control <- rpa_control_scenario(alpha = 0.5, beta = 0.5) +
  rpa_control_preference(
    ftype = "customized",
    spref = "pow(outs, 2) + 1",
    tpref = "pow(ins, 2) + 1"
  )


control <- rpa_control_scenario(alpha = 1) +
  rpa_control_edgeweight(
    sampler = function(n) rgamma(n, shape = 5, scale = 0.2)
  )

Converts an adjacency matrix to edgelist and edgeweight using the igraph package.

Description

Converts an adjacency matrix to edgelist and edgeweight using the igraph package.

Usage

adj_to_edgelist(adj, directed = TRUE, weighted = TRUE)

Arguments

Value

A list of edgelist, edgeweight and directed.

Creates a wdnet object using an adjacency matrix

Description

Creates a wdnet object using an adjacency matrix

Usage

adj_to_wdnet(adj, directed = TRUE, weighted = TRUE, nodegroup, ...)

Arguments

Value

A wdnet object with the specified adj.

Examples

adj <- matrix(c(0, 1, 2, 0), nrow = 2, ncol = 2, byrow = TRUE)
adj_to_wdnet(adj = adj, directed = TRUE, weighted = FALSE)

Compute the assortativity coefficient(s) for a network.

Description

Compute the assortativity coefficient(s) for a network.

Usage

assortcoef(netwk, edgelist, edgeweight, adj, directed, f1, f2)

Arguments

Value

Assortativity coefficient for undirected networks, or a list of four assortativity coefficients for directed networks.

Note

When the adjacency matrix is binary (i.e., directed but unweighted networks), assortcoef returns the assortativity coefficient proposed in Foster et al. (2010).

References

• Foster, J.G., Foster, D.V., Grassberger, P. and Paczuski, M. (2010). Edge direction and the structure of networks. Proceedings of the National Academy of Sciences of the United States, 107(24), 10815–10820.

• Yuan, Y. Zhang, P. and Yan, J. (2021). Assortativity coefficients for weighted and directed networks. Journal of Complex Networks, 9(2), cnab017.

Examples

set.seed(123)
control <- rpa_control_edgeweight(
  sampler = function(n) rgamma(n, shape = 5, scale = 0.2)
)
netwk <- rpanet(nstep = 10^4, control = control)
ret <- assortcoef(netwk)
ret <- assortcoef(
  edgelist = netwk$edgelist,
  edgeweight = netwk$edge.attr$weight,
  directed = TRUE
)

Centrality measures

Description

Computes the centrality measures of the nodes in a weighted and directed network.

Usage

centrality(
  netwk,
  adj,
  edgelist,
  edgeweight,
  directed = TRUE,
  measure = c("degree", "closeness", "wpr"),
  degree.control = list(alpha = 1, mode = "out"),
  closeness.control = list(alpha = 1, mode = "out", method = "harmonic", distance =
    FALSE),
  wpr.control = list(gamma = 0.85, theta = 1, prior.info = NULL)
)

Arguments

Value

A list of node names and associated centrality measures

Note

The degree-based centrality measure is an extension of function strength in package igraph and an alternative of function degree_w in package tnet.

The closeness centrality measure is an extension of function closeness in package igraph and function closeness_w in package tnet. The method of computing distances between vertices is the Dijkstra's algorithm.

The weighted PageRank centrality measure is an extension of function page_rank in package igraph.

References

• Dijkstra, E.W. (1959). A note on two problems in connexion with graphs. Numerische Mathematik, 1, 269–271.

• Newman, M.E.J. (2003). The structure and function of complex networks. SIAM review, 45(2), 167–256.

• Opsahl, T., Agneessens, F., Skvoretz, J. (2010). Node centrality in weighted networks: Generalizing degree and shortest paths. Social Networks, 32, 245–251.

• Zhang, P., Wang, T. and Yan, J. (2022) PageRank centrality and algorithms for weighted, directed networks with applications to World Input-Output Tables. Physica A: Statistical Mechanics and its Applications, 586, 126438.

• Zhang, P., Zhao, J. and Yan, J. (2020+) Centrality measures of networks with application to world input-output tables

Examples

## Generate a network according to the Erd\"{o}s-Renyi model of order 20
## and parameter p = 0.3
edge_ER <- rbinom(400, 1, 0.3)
weight_ER <- sapply(edge_ER, function(x) x * sample(3, 1))
adj_ER <- matrix(weight_ER, 20, 20)
mydegree <- centrality(
  adj = adj_ER,
  measure = "degree", degree.control =
    list(alpha = 0.8, mode = "in")
)
myclose <- centrality(
  adj = adj_ER,
  measure = "closeness", closeness.control =
    list(alpha = 0.8, mode = "out", method = "harmonic", distance = FALSE)
)
mywpr <- centrality(
  adj = adj_ER,
  measure = "wpr", wpr.control =
    list(gamma = 0.85, theta = 0.75)
)

Closeness centrality

Description

Compute the closeness centrality measures of the vertices in a weighted and directed network represented through its adjacency matrix.

Usage

closeness_c(
  adj,
  alpha = 1,
  mode = "out",
  method = "harmonic",
  distance = FALSE
)

Arguments

Value

a list of node names and associated closeness centrality measures

Note

Function closeness_c is an extension of function closeness in package igraph and function closeness_w in package tnet. The method of computing distances between vertices is the Dijkstra's algorithm.

References

• Dijkstra, E.W. (1959). A note on two problems in connexion with graphs. Numerische Mathematik, 1, 269–271.

• Newman, M.E.J. (2003). The structure and function of complex networks. SIAM review, 45(2), 167–256.

• Opsahl, T., Agneessens, F., Skvoretz, J. (2010). Node centrality in weighted networks: Generalizing degree and shortest paths. Social Networks, 32, 245–251.

• Zhang, P., Zhao, J. and Yan, J. (2020+) Centrality measures of networks with application to world input-output tables

Directed clustering coefficient

Description

Compute the clustering coefficient of a weighted and directed network.

Usage

clustcoef(
  netwk,
  edgelist,
  edgeweight,
  adj,
  directed = TRUE,
  method = c("Clemente", "Fagiolo"),
  isolates = 0
)

Arguments

Value

Lists of local clustering coefficients (in terms of a vector), global clustering coefficient (in terms of a scalar) and number of weighted directed triangles (in terms of a vector) based on total, in, out, middleman (middle), or cycle triplets.

Note

Self-loops (if exist) are removed prior to the computation of clustering coefficient. When the adjacency matrix is symmetric (i.e., undirected but possibly unweighted networks), clustcoef returns local and global clustering coefficients proposed by Barrat et al. (2010).

References

• Barrat, A., Barthelemy, M., Pastor-Satorras, R. and Vespignani, A. (2004). The architecture of complex weighted networks. Proceedings of National Academy of Sciences of the United States of America, 101(11), 3747–3752.

• Clemente, G.P. and Grassi, R. (2018). Directed clustering in weighted networks: A new perspective. Chaos, Solitons & Fractals, 107, 26–38.

• Fagiolo, G. (2007). Clustering in complex directed networks. Physical Review E, 76, 026107.

Examples

## Generate a network according to the Erd\"{o}s-Renyi model of order 20
## and parameter p = 0.3
edge_ER <- rbinom(400, 1, 0.3)
weight_ER <- sapply(edge_ER, function(x) x * sample(3, 1))
adj_ER <- matrix(weight_ER, 20, 20)
mycc <- clustcoef(adj = adj_ER, method = "Clemente")
system.time(mycc)

Compile preference functions via RcppXPtrUtils.

Description

Compile preference functions via RcppXPtrUtils.

Usage

compile_pref_func(preference, directed)

Arguments

Value

Returns the input list and their corresponding external pointers.

Creates a wdnet object from input data.

Description

This function creates a wdnet object from edgelist and edgeweight or adj or returns the existing wdnet object. For internal usage.

Usage

create_wdnet(
  netwk,
  edgelist,
  edgeweight,
  nodegroup,
  directed,
  adj,
  weighted,
  ...
)

Arguments

Value

A wdnet object.

Parameters passed to CVXR::solve().

Description

Defined for the convex optimization problems for solving eta.

Usage

cvxr_control(
  solver = "ECOS",
  ignore_dcp = FALSE,
  warm_start = FALSE,
  verbose = FALSE,
  parallel = FALSE,
  gp = FALSE,
  feastol = 1e-05,
  reltol = 1e-05,
  abstol = 1e-05,
  num_iter = NULL,
  ...
)

Arguments

Value

A list containing the parameters.

Examples

control <- cvxr_control(solver = "OSQP", abstol = 1e-5)

Degree-based centrality

Description

Compute the degree centrality measures of the vertices in a weighted and directed network represented through its adjacency matrix.

Usage

degree_c(adj, alpha = 1, mode = "out")

Arguments

Value

a list of node names and associated degree centrality measures

Note

Function degree_c is an extension of function strength in package igraph and an alternative of function degree_w in package tnet. Function degree_c uses adjacency matrix as input.

References

• Opsahl, T., Agneessens, F., Skvoretz, J. (2010). Node centrality in weighted networks: Generalizing degree and shortest paths. Social Networks, 32, 245–251.

• Zhang, P., Zhao, J. and Yan, J. (2020+) Centrality measures of networks with application to world input-output tables

Degree preserving rewiring.

Description

Rewire a given network to have predetermined assortativity coefficient(s) while preserving node degree.

Usage

dprewire(
  netwk,
  edgelist,
  directed,
  adj,
  target.assortcoef = list(outout = NULL, outin = NULL, inout = NULL, inin = NULL),
  control = list(iteration = 200, nattempts = NULL, history = FALSE, cvxr_control =
    cvxr_control(), eta.obj = function(x) 0),
  eta
)

Arguments

Details

The algorithm first solves for an appropriate eta using target.assortcoef, eta.obj, and cvxr_control, then proceeds to the rewiring process and rewire the network towards the solved eta. If eta is given, the algorithm will skip the first step. This function only works for unweighted networks.

Each rewiring attempt samples two rows from edgelist, for instance Edge 1:(v_1, v_2) and Edge 2:(v_3, v_4). For directed networks, if the rewiring attempt is accepted, the sampled edges are rewired as (v_1, v_4), (v_3, v_2); for undirected networks, the algorithm try to rewire the sampled edges as {v_1, v_4}, {v_3, v_2} (type 1) or {v_1, v_3}, {v_2, v_4} (type 2), each with probability 1/2.

Value

Rewired network; assortativity coefficient(s) after each iteration; rewiring history (including the index of sampled edges and rewiring result) and solver results.

Examples

set.seed(123)
netwk1 <- rpanet(1e4, control = rpa_control_scenario(
  alpha = 0.4, beta = 0.3, gamma = 0.3
))
## rewire a directed network
target.assortcoef <- list("outout" = -0.2, "outin" = 0.2)
ret1 <- dprewire(
  netwk = netwk1,
  target.assortcoef = target.assortcoef,
  control = list(iteration = 200)
)
plot(ret1$assortcoef$Iteration, ret1$assortcoef$"outout")
plot(ret1$assortcoef$Iteration, ret1$assortcoef$"outin")

## rewire an undirected network
netwk2 <- rpanet(1e4,
  control = rpa_control_scenario(
    alpha = 0.3, beta = 0.1, gamma = 0.3, xi = 0.3
  ),
  initial.network = list(
    directed = FALSE)
)
ret2 <- dprewire(
  netwk = netwk2,
  target.assortcoef = 0.3,
  control = list(
    iteration = 300, eta.obj = CVXR::norm2,
    history = TRUE
  )
)
plot(ret2$assortcoef$Iteration, ret2$assortcoef$Value)

Range of assortativity coefficients.

Description

The assortativity coefficient of a given network may not reach all the values between -1 and 1 via degree preserving rewiring. This function calculates the range of assortativity coefficients achievable through degree preserving rewiring. The algorithm is designed for unweighted networks.

Usage

dprewire.range(
  netwk,
  edgelist,
  adj,
  directed,
  which.range = c("outout", "outin", "inout", "inin"),
  control = cvxr_control(),
  target.assortcoef = list(outout = NULL, outin = NULL, inout = NULL, inin = NULL)
)

Arguments

Details

The ranges are computed using convex optimization. The optimization problems are defined and solved via the R package CVXR. For undirected networks, the function returns the range of the assortativity coefficient. For directed networks, the function computes the range of which.range while other assortativity coefficients are restricted through target.assortcoef.

Value

Returns the range of the selected assortativity coefficient and the results from the solver.

Examples

set.seed(123)
netwk <- rpanet(5e3,
  control =
    rpa_control_scenario(alpha = 0.5, beta = 0.5)
)
ret1 <- dprewire.range(
  netwk = netwk, which.range = "outin",
  target.assortcoef = list("outout" = c(-0.3, 0.3), "inout" = 0.1)
)
ret1$range

Degree preserving rewiring for directed networks

Description

Degree preserving rewiring towards the target structure eta.

Usage

dprewire_directed(
  edgelist,
  eta,
  iteration = 200,
  nattempts,
  rewire.history = FALSE
)

Arguments

Value

Rewired edgelist, degree based assortativity coefficients after each iteration, rewiring history (including the index of sampled edges and rewiring result). For each rewiring attempt, two rows are sampled form the edgelist, for example Edge1:(v_1, v_2) and Edge2:(v_3, v_4). If the rewiring attempt is accepted, the sampled edges are replaced as (v_1, v_4), (v_3, v_2).

Degree preserving rewiring process for directed networks.

Description

Degree preserving rewiring process for directed networks.

Usage

dprewire_directed_cpp(
  iteration,
  nattempts,
  tnode,
  sout,
  sin,
  tout,
  tin,
  index_s,
  index_t,
  eta,
  rewire_history
)

Arguments

Value

Returns target node sequence, four directed assortativity coefficients after each iteration, and rewire history.

Degree preserving rewiring for undirected networks

Description

Degree preserving rewiring towards the target structure eta.

Usage

dprewire_undirected(
  edgelist,
  eta,
  iteration = 200,
  nattempts,
  rewire.history = FALSE
)

Arguments

Value

Rewired edgelist, assortativity coefficient after each iteration, and rewiring history (including the index of sampled edges and rewiring result). For each rewiring attempt, two rows are sampled from the edgelist, for example Edge1:{v_1, v_2} and Edge2:{v_3, v_4}, the function try to rewire the sampled edges as {v_1, v_4}, {v_3, v_2} (rewire type 1) or {v_1, v_3}, {v_2, v_4} (rewire type 2) with probability 1/2.

Degree preserving rewiring process for undirected networks.

Description

Degree preserving rewiring process for undirected networks.

Usage

dprewire_undirected_cpp(
  iteration,
  nattempts,
  node1,
  node2,
  degree1,
  degree2,
  index1,
  index2,
  e,
  rewire_history
)

Arguments

Value

Returns node sequences, assortativity coefficient after each iteration, and rewiring history.

Compute the assortativity coefficient of a weighted and directed network.

Description

Compute the assortativity coefficient of a weighted and directed network.

Usage

dw_assort(adj, type = c("outin", "inin", "outout", "inout"))

Arguments

Value

a scalar of assortativity coefficient

Note

When the adjacency matrix is binary (i.e., directed but unweighted networks), dw_assort returns the assortativity coefficient proposed in Foster et al. (2010).

References

• Foster, J.G., Foster, D.V., Grassberger, P. and Paczuski, M. (2010). Edge direction and the structure of networks. Proceedings of the National Academy of Sciences of the United States, 107(24), 10815–10820.

• Yuan, Y. Zhang, P. and Yan, J. (2021). Assortativity coefficients for weighted and directed networks. Journal of Complex Networks, 9(2), cnab017.

Feature based assortativity coefficient

Description

Node feature based assortativity coefficients for weighted and directed networks.

Usage

dw_feature_assort(netwk, f1, f2)

Arguments

Value

Directed weighted assortativity coefficients between source nodes' f1 (or f2) and target nodes' f2(or f1).

Examples

set.seed(123)
adj <- matrix(rbinom(400, 1, 0.2) * sample(1:3, 400, replace = TRUE), 20, 20)
f1 <- runif(20)
f2 <- abs(rnorm(20))
ret <- assortcoef(adj = adj, f1 = f1, f2 = f2)

Convert edgelist and edgeweight to adjacency matrix.

Description

Convert edgelist and edgeweight to adjacency matrix.

Usage

edgelist_to_adj(edgelist, edgeweight, directed = TRUE)

Arguments

Value

Returns an adjacency matrix.

Creates a wdnet object using edgelist.

Description

Creates a wdnet object using edgelist.

Usage

edgelist_to_wdnet(edgelist, edgeweight, directed, nodegroup, ...)

Arguments

Value

A wdnet object with the specified edgelist, edgeweight and directed.

Examples

edgelist <- matrix(c(1, 2, 2, 3, 3, 1), ncol = 2, byrow = TRUE)
edgeweight <- c(1, 2, 3)
nodegroup <- c(1, 1, 2)
netwk <- edgelist_to_wdnet(
  edgelist = edgelist,
  edgeweight = edgeweight,
  directed = TRUE,
  nodegroup = nodegroup
)

Fill edgeweight into the adjacency matrix. Defined for function edgelist_to_adj.

Description

Fill edgeweight into the adjacency matrix. Defined for function edgelist_to_adj.

Usage

fill_weight_cpp(adj, edgelist, edgeweight)

Arguments

Value

Adjacency matrix with edge weight.

Fill missing nodes in the node sequence. Defined for wdnet::rpanet.

Description

Fill missing nodes in the node sequence. Defined for wdnet::rpanet.

Usage

find_node_cpp(nodes, edges)

Arguments

Value

Source/target nodes.

Fill missing values in node sequence. Defined for wdnet::rpanet.

Description

Fill missing values in node sequence. Defined for wdnet::rpanet.

Usage

find_node_undirected_cpp(node1, node2, start_edge, end_edge)

Arguments

Value

Node sequence.

Get the constraints for the optimization problem. This function is defined for get_eta_directed().

Description

Get the constraints for the optimization problem. This function is defined for get_eta_directed().

Usage

get_constr(constrs, target.assortcoef, rho)

Arguments

Value

A list of updated constraints.

Get the node-level joint distributions and some empirical distributions with given edgelist.

Description

Get the node-level joint distributions and some empirical distributions with given edgelist.

Usage

get_dist(edgelist, directed = TRUE, joint_dist = FALSE)

Arguments

Value

A list of distributions and degree vectors.

Compute edge-level distributions for directed networks with respect to desired assortativity level(s).

Description

Compute edge-level distributions for directed networks with respect to desired assortativity level(s).

Usage

get_eta_directed(
  edgelist,
  target.assortcoef = list(outout = NULL, outin = NULL, inout = NULL, inin = NULL),
  eta.obj = function(x) 0,
  which.range,
  control = cvxr_control()
)

Arguments

Value

Assortativity coefficients and joint distributions. If which.range is specified, the range of the interested coefficient and the corresponding joint distributions will be returned, provided the predetermined target.assortcoef is satisfied.

Compute edge-level distribution for undirected networks with respect to desired assortativity level.

Description

Compute edge-level distribution for undirected networks with respect to desired assortativity level.

Usage

get_eta_undirected(
  edgelist,
  target.assortcoef = NULL,
  eta.obj = function(x) 0,
  control = cvxr_control()
)

Arguments

Value

Assortativity level and corresponding edge-level distribution.

Get the value of an object from the optimization problem. This function is defined for get_eta_directed().

Description

Get the value of an object from the optimization problem. This function is defined for get_eta_directed().

Usage

get_values(object, result, mydist)

Arguments

Value

Returns the value of the object.

Converts an igraph object to a wdnet object

Description

Converts an igraph object to a wdnet object

Usage

igraph_to_wdnet(g)

Arguments

Value

A wdnet object.

Examples

g <- igraph::sample_pa(50)
netwk <- igraph_to_wdnet(g)

Checks whether the input is a rpacontrol object

Description

Checks whether the input is a rpacontrol object

Usage

is_rpacontrol(control)

Arguments

Value

Logical, TRUE if the input is a rpacontrol object.

Checks if the input is a wdnet object

Description

Checks if the input is a wdnet object

Usage

is_wdnet(netwk)

Arguments

Value

Logical, TRUE if argument netwk is a wdnet object.

Examples

netwk <- rpanet(nstep = 1e3)
is_wdnet(netwk)

Aggregate edgeweight into nodes' strength.

Description

Aggregate edgeweight into nodes' strength.

Usage

node_strength_cpp(snode, tnode, weight, nnode, weighted = TRUE)

Arguments

Value

Out-strength and in-strength.

Plots the input network

Description

Plots the input network via igraph::plot.igraph().

Usage

## S3 method for class 'wdnet'
plot(x, ...)

Arguments

Value

Returns NULL, invisibly.

Prints rpacontrol objects

Description

These functions print rpacontrol objects in the terminal. print.rpacontrol() shows only the current controls, whereas summary.rpacontrol() includes both specified controls and the unspecified controls that use default values.

Usage

## S3 method for class 'rpacontrol'
print(x, ...)

## S3 method for class 'rpacontrol'
summary(object, ...)

Arguments

Value

Returns the controls invisibly.

Examples

control <- rpa_control_scenario()
print(control)

Prints the input network

Description

These functions print a network to the terminal.

Usage

## S3 method for class 'wdnet'
print(x, node.attrs = TRUE, edge.attrs = TRUE, max.lines = 5, ...)

## S3 method for class 'wdnet'
summary(object, ...)

Arguments

Details

summary.wdnet prints the number of nodes and edges, preference functions, and whether the network is directed, weighted. print.wdnet prints the same information, and also lists some edges and node attributes, if available. Edge scenarios are 0: from initial network; 1: alpha; 2: beta; 3: gamma; 4: xi; 5; rho; 6: reciprocal.

Prints rpacontrol in terminal

Description

Prints rpacontrol in terminal

Usage

print_control_details(x, control_name)

Arguments

Value

Returns NULL invisibly.

Prints rpa_control_edgeweight() in terminal

Description

Prints rpa_control_edgeweight() in terminal

Usage

print_control_edgeweight(control)

Arguments

Value

Returns NULL invisibly.

Prints rpa_control_newedge() in terminal

Description

Prints rpa_control_newedge() in terminal

Usage

print_control_newedge(control)

Arguments

Value

Returns NULL invisibly.

Prints rpa_control_preference() in terminal

Description

Prints rpa_control_preference() in terminal

Usage

print_control_preference(control, directed)

Arguments

Value

Returns NULL invisibly.

Prints rpa_control_reciprocal() in terminal

Description

Prints rpa_control_reciprocal() in terminal

Usage

print_control_reciprocal(control)

Arguments

Value

Returns NULL invisibly.

Prints rpa_control_scenario() in terminal

Description

Prints rpa_control_scenario() in terminal

Usage

print_control_scenario(control)

Arguments

Value

Returns NULL invisibly.

Default controls for rpanet

Description

Default controls for rpanet

Usage

rpa_control_default()

Value

Returns a list of default controls.

Control weight of new edges. Defined for rpanet.

Description

Control weight of new edges. Defined for rpanet.

Usage

rpa_control_edgeweight(sampler = NULL)

Arguments

Value

A list of class rpacontrol containing the sampler function.

Examples

# Sample edge weights from Gamma(5, 0.2).
my_gamma <- function(n) rgamma(n, shape = 5, scale = 0.2)
control <- rpa_control_edgeweight(
  sampler = my_gamma
)

Control new edges in each step. Defined for rpanet.

Description

Control new edges in each step. Defined for rpanet.

Usage

rpa_control_newedge(
  sampler = NULL,
  snode.replace = TRUE,
  tnode.replace = TRUE,
  node.replace = TRUE
)

Arguments

Value

A list of class rpacontrol with components sampler, snode.replace, tnode.replace and node.replace with meanings as explained under 'Arguments'.

Examples

my_rpois <- function(n) rpois(n, lambda = 2) + 1
control <- rpa_control_newedge(
  sampler = my_rpois,
  node.replace = FALSE
)

Set preference function(s). Defined for rpanet.

Description

Set preference function(s). Defined for rpanet.

Usage

rpa_control_preference(
  ftype = c("default", "customized"),
  sparams = c(1, 1, 0, 0, 1),
  tparams = c(0, 0, 1, 1, 1),
  params = c(1, 1),
  spref = "outs + 1",
  tpref = "ins + 1",
  pref = "s + 1"
)

Arguments

Details

If choosing customized preference functions, spref, tpref and pref will be used and the network generation method must be "binary" or "linear". spref (tpref) defines the source (target) preference function, it can be a character expression or an object of class XPtr.

• Character expression; it must be a one-line C++ style expression of outs (node out-strength) and ins (node in-strength). For example, "pow(outs, 2) + 1", "pow(outs, 2) + pow(ins, 2) + 1", etc. The expression will be used to define an XPtr via RcppXPtrUtils::cppXPtr. The XPtr will be passed to the network generation function. The expression must not have variables other than outs and ins.

• 'XPtr' an external pointer wrapped in an object of class XPtr defined via RcppXPtrUtils::cppXPtr. An example for defining an XPtr with C++ source code is included in Examples. For more information about passing function pointers, see https://gallery.rcpp.org/articles/passing-cpp-function-pointers-rcppxptrutils/. Please note the supplied C++ function accepts two double arguments and returns a double. The first and second arguments represent node out- and in-strength, respectively. Note that the XPtr will be invalid and cannot be used to control network generation in another separate R session. Therefore, we recommend preserving the source code of your preference function for future use.

pref is defined analogously. If using character expression, it must be a one-line C++ style expression of s (node strength). If using XPtr, the supplied C++ function accepts only one double argument and returns a double.

Value

A list of class rpacontrol with components ftype, sparams, tparams, params or ftype, spref, tpref, pref with function pointers spref.pointer, tpref.pointer, pref.pointer.

Examples

# Set source preference as out-strength^2 + in-strength + 1,
# target preference as out-strength + in-strength^2 + 1.
# 1. use default preference functions
ctr1 <- rpa_control_preference(
  ftype = "default",
  sparams = c(1, 2, 1, 1, 1), tparams = c(1, 1, 1, 2, 1)
)
# 2. use character expressions
ctr2 <- rpa_control_preference(
  ftype = "customized",
  spref = "pow(outs, 2) + ins + 1", tpref = "outs + pow(ins, 2) + 1"
)
# 3. define XPtr's with C++ source code
spref.pointer <- RcppXPtrUtils::cppXPtr(
  code =
    "double spref(double outs, double ins) {return pow(outs, 2) + ins + 1;}"
)
tpref.pointer <- RcppXPtrUtils::cppXPtr(
  code =
    "double tpref(double outs, double ins) {return outs + pow(ins, 2) + 1;}"
)
ctr3 <- rpa_control_preference(
  ftype = "customized",
  spref = spref.pointer,
  tpref = tpref.pointer
)
ret <- rpanet(1e5, control = ctr3)

Control reciprocal edges. Defined for rpanet.

Description

Control reciprocal edges. Defined for rpanet.

Usage

rpa_control_reciprocal(
  group.prob = NULL,
  recip.prob = NULL,
  selfloop.recip = FALSE
)

Arguments

Value

A list of class rpacontrol with components group.prob, recip.prob, and selfloop.recip with meanings as explained under 'Arguments'.

Examples

control <- rpa_control_reciprocal(
  group.prob = c(0.4, 0.6),
  recip.prob = matrix(runif(4), ncol = 2)
)

Control edge scenarios. Defined for rpanet.

Description

Control edge scenarios. Defined for rpanet.

Usage

rpa_control_scenario(
  alpha = 1,
  beta = 0,
  gamma = 0,
  xi = 0,
  rho = 0,
  beta.loop = TRUE,
  source.first = TRUE
)

Arguments

Value

A list of class rpacontrol with components alpha, beta, gamma, xi, rho, beta.loop and source.first with meanings as explained under 'Arguments'.

Examples

control <- rpa_control_scenario(alpha = 0.5, beta = 0.5, beta.loop = FALSE)

rpacontrol: Controls the Preferential Attachment (PA) Network Generation Process

Description

The rpacontrol object is designed to control the Preferential Attachment (PA) network generation process within the rpanet() function. It can have the following components:

• scenario: controls the edge scenarios at each step. For more information, please refer to rpa_control_scenario().

• edgeweight: controls the weight of the edges; see rpa_control_edgeweight() for details.

• newedge: controls the creation of new edges at each step; see rpa_control_newedge() for details.

• preference: sets preference functions; see rpa_control_preference() for details.

• reciprocal: controls the creation of reciprocal edges; see rpa_control_reciprocal() for details.

Generate PA networks.

Description

Generate preferential attachment (PA) networks with linear or non-linear preference functions.

Usage

rpanet(
  nstep,
  initial.network = list(edgelist = matrix(c(1, 2), nrow = 1), edgeweight = 1, directed =
    TRUE),
  control,
  method = c("binary", "linear", "bagx", "bag")
)

Arguments

Value

Returns a wdnet object that includes the following components:

• directed: Logical, whether the network is directed.

• weighted: Logical, whether the network is weighted.

• edgelist: A two-column matrix representing the edges.

• edge.attr: A data frame including edge weights and edge scenarios (0: from initial network; 1: alpha; 2: beta; 3: gamma; 4: xi; 5; rho; 6: reciprocal edge).

• node.attr: A data frame including node out- and in-strength, node source and target preference scores (for directed networks), node strength and preference scores (for undirected networks), and node group (if applicable).

• newedge: The number of new edges at each step, including reciprocal edges.

• control: An rpacontrol object that is used to generate the network.

Note

The binary method implements binary search algorithm; linear represents linear search algorithm; bag method implements the algorithm from Wan et al. (2017); bagx puts all the edges into a bag, then samples edges and find the source/target node of the sampled edge.

References

• Wan P, Wang T, Davis RA, Resnick SI (2017). Fitting the Linear Preferential Attachment Model. Electronic Journal of Statistics, 11(2), 3738–3780.

Examples

# Control edge scenario and edge weight through rpa_control_scenario()
# and rpa_control_edgeweight(), respectively,
# while keeping rpa_control_newedge(),
# rpa_control_preference() and rpa_control_reciprocal() as default.
set.seed(123)
control <- rpa_control_scenario(alpha = 0.5, beta = 0.5) +
  rpa_control_edgeweight(
    sampler = function(n) rgamma(n, shape = 5, scale = 0.2)
  )
ret1 <- rpanet(nstep = 1e3, control = control)

# In addition, set node groups and probability of creating reciprocal edges.
control <- control + rpa_control_reciprocal(
  group.prob = c(0.4, 0.6),
  recip.prob = matrix(runif(4), ncol = 2)
)
ret2 <- rpanet(nstep = 1e3, control = control)

# Further, set the number of new edges in each step as Poisson(2) + 1 and use
# ret2 as a seed network.
control <- control + rpa_control_newedge(
  sampler = function(n) rpois(n, lambda = 2) + 1
)
ret3 <- rpanet(nstep = 1e3, initial.network = ret2, control = control)

Preferential attachment algorithm for simple situations, i.e., edge weight equals 1, each step adds one new edge.

Description

Preferential attachment algorithm for simple situations, i.e., edge weight equals 1, each step adds one new edge.

Usage

rpanet_bag_cpp(
  snode,
  tnode,
  scenario,
  nnode,
  nedge,
  delta_out,
  delta_in,
  directed
)

Arguments

Value

Returns a list that includes the total number of nodes, sequences of source and target nodes.

Preferential attachment network generation.

Description

Preferential attachment network generation.

Usage

rpanet_binary_directed(
  nstep,
  m,
  new_node_id,
  new_edge_id,
  source_node,
  target_node,
  outs,
  ins,
  edgeweight,
  scenario,
  sample_recip,
  node_group,
  spref_vec,
  tpref_vec,
  control
)

Arguments

Value

Sampled network.

Preferential attachment network generation.

Description

Preferential attachment network generation.

Usage

rpanet_binary_undirected_cpp(
  nstep,
  m,
  new_node_id,
  new_edge_id,
  node_vec1,
  node_vec2,
  s,
  edgeweight,
  scenario,
  pref_vec,
  control
)

Arguments

Value

Sampled network.

Internal functions for generating PA networks

Description

These functions generate a PA network with linear (rpanet_simple) or non-linear (rpanet_general) preference functions

Usage

rpanet_general(
  nstep,
  initial.network,
  control,
  m,
  sum_m,
  w,
  nnode,
  nedge,
  method,
  sample.recip
)

rpanet_simple(
  nstep,
  initial.network,
  control,
  m,
  sum_m,
  w,
  ex_node,
  ex_edge,
  method
)

Arguments

Value

Returns a wdnet object that includes the following components:

• directed: Logical, whether the network is directed.

• weighted: Logical, whether the network is weighted.

• edgelist: A two-column matrix representing the edges.

• edge.attr: A data frame including edge weights and edge scenarios (0: from initial network; 1: alpha; 2: beta; 3: gamma; 4: xi; 5; rho; 6: reciprocal edge).

• node.attr: A data frame including node out- and in-strength, node source and target preference scores (for directed networks), node strength and preference scores (for undirected networks), and node group (if applicable).

• newedge: The number of new edges at each step, including reciprocal edges.

• control: An rpacontrol object that is used to generate the network.

Preferential attachment network generation.

Description

Preferential attachment network generation.

Usage

rpanet_linear_directed_cpp(
  nstep,
  m,
  new_node_id,
  new_edge_id,
  source_node,
  target_node,
  outs,
  ins,
  edgeweight,
  scenario,
  sample_recip,
  node_group,
  spref_vec,
  tpref_vec,
  control
)

Arguments

Value

Sampled network.

Preferential attachment network generation.

Description

Preferential attachment network generation.

Usage

rpanet_linear_undirected_cpp(
  nstep,
  m,
  new_node_id,
  new_edge_id,
  node_vec1,
  node_vec2,
  s,
  edgeweight,
  scenario,
  pref_vec,
  control
)

Arguments

Value

Sampled network.

Uniformly draw a node from existing nodes for each time step. Defined for wdnet::rpanet().

Description

Uniformly draw a node from existing nodes for each time step. Defined for wdnet::rpanet().

Usage

sample_node_cpp(total_node)

Arguments

Value

Sampled nodes.

Converts a wdnet object to an igraph object

Description

Converts a wdnet object to an igraph object

Usage

wdnet_to_igraph(netwk)

Arguments

Value

An igraph object.

Examples

netwk <- rpanet(nstep = 1e3)
g <- wdnet_to_igraph(netwk)

Weighted PageRank centrality

Description

Compute the weighted PageRank centrality measures of the vertices in a weighted and directed network represented through its adjacency matrix.

Usage

wpr(adj, gamma = 0.85, theta = 1, prior.info)

Arguments

Value

a list of node names with corresponding weighted PageRank scores

Note

Function wpr is an extension of function page_rank in package igraph.

References

• Zhang, P., Wang, T. and Yan, J. (2022) PageRank centrality and algorithms for weighted, directed networks with applications to World Input-Output Tables. Physica A: Statistical Mechanics and its Applications, 586, 126438.