ILSM (version 1.1.0.1)

node_icc: Interconnection centrality for connector nodes in a tripartite network

Description

Calculating interconnection centrality (degree, betweenness and closeness) specified for connector nodes in a tripartite network.

Usage

node_icc(network.or.subnet_mat1, subnet_mat2 = NULL, weighted = FALSE)

Value

Return a data frame with interconnection degree, betweenness and closeness for connector nodes.

Arguments

network.or.subnet_mat1

An igraph object or matrix. An "igraph" object with node attribute 'level' or a matrix representing one subnetwork. See details.

subnet_mat2

A matrix representing one subnetwork.

weighted

Logical. If TRUE, link strengths of connector nodes are used. Default to FALSE.

Details

In this package, a tripartite network contains three groups of nodes (a-nodes,b-nodes,c-nodes) and two subnetworks (P includes the links between a-nodes and b-nodes, Q includes the links between b-nodes and c-nodes). Connector nodes belong to b-nodes. This function calculates interconnection degree, betweenness and closeness centrality for connector nodes.

• For binary networks, Interconnection degree of each connector species is defined as the product of its degree values from two subnetworks.

• Interconnection betweenness is defined by the number of shortest paths from a-nodes to c-nodes going through connector species, \(\sum_{\substack{i \in a,\, j \in c \\ i \neq j}} \frac{g_{ivj}}{g_{ij}}\), where \(g_{ij}\) is the total number of shortest paths between node \(i\) from a-nodes and \(j\) from c-nodes while \(g_{ivj}\) is the number of those shortest paths which pass through connector species \(v\).

• Interconnection closeness is defined by the inverse of the sum of distances from connector species to both a-nodes and c-nodes, \(1/(\sum_{v \neq i, i \in a \cup c} d_{vi})\), where \(d_{vi}\) is the distance between connector species \(v\) and species \(i\) from a-nodes and c-nodes. For weighted networks, interaction strengths are used in the calculation of weighted degree, shorest path, and distance.

network.or.subnet_mat1 and subnet_mat2

Two types of inputs network.or.subnet_mat1 can be processed:

• An "igraph" object with node attribute 'level' (0 for a-nodes, 1 for b-nodes,2 for c-nodes). If the input is a weighted network, the edge should have a 'weight' attribute.

• Or a matrix representing subnetwork P, and must be input with subnet_mat2 representing subnetwork Q.

If the inputs are two matrices, please make sure the rows of network.or.subnet_mat1 and subnet_mat2 both represent the groups of connector species,i.e, the b-group species. If both matrices have row names, then the function matches row names to produce connector nodes. Otherwise, row numbers are assigned as row names.

Examples

## generate a random tripartite network
set.seed(12)
Net <- build_toy_net(11,15,16,0.2)

data(PPH_Coltparkmeadow)
Net <- PPH_Coltparkmeadow
node_icc(Net)
set.seed(13)
library(igraph)
E(Net)$weight<-runif(length(E(Net)),0.1,1)#random weights assigned
node_icc(Net,weighted=TRUE)

##input as binary matrices,with row names.
set.seed(12)
md1 <- matrix(sample(c(0,1),5*8,replace=TRUE),5,8,
       dimnames = list(paste0("b",1:5),paste0("c",1:8)))
md2 <- matrix(sample(c(0,1),20*30,replace=TRUE),20,30,
       dimnames = list(paste0("b",1:20),paste0("a",1:30)))
node_icc(md1,md2)

##input as weighted matrices,with row numbers as row names.
set.seed(17)
mdw1 <- matrix(sample(c(rep(0,20),runif(20,0,1))),5,8)
mdw2 <- matrix(sample(c(rep(0,500),runif(100,0,1))),20,30)
node_icc(mdw1,mdw2)
node_icc(mdw1,mdw2,weighted=TRUE)