computeTMDens: Compute Level-Specific Graph Density for Two-Mode Networks
In dream: Dynamic Relational Event Analysis and Modeling

computeTMDens

R Documentation

Compute Level-Specific Graph Density for Two-Mode Networks

Description

This function computes the density of a two-mode network following Wasserman and Faust (1994) and Knoke and Yang (2020). The density is computed based on the specified level. That is, in an affiliation matrix, density can be computed on the symmetric g x g matrix of co-membership for the level 1 actors or on the symmetric h x h matrix of shared actors for level 2 groups.

Usage

computeTMDens(net, binary = FALSE, level1 = TRUE)

Arguments

`net`	A two-mode adjacency matrix.
`binary`	TRUE/FALSE. TRUE indicates that the transposed matrices will be binarized (see Wasserman and Faust 1995: 316). FALSE indicates that the transposed matrices will not be binarized. Set to FALSE by default.
`level1`	TRUE/FALSE. TRUE indicates that the graph density will be computed for level 1 nodes. FALSE indicates that the graph density will be computed for level 2 nodes. Set to FALSE by default.

Details

Following Wasserman and Faust (1994) and Knoke and Yang (2020), the computation of density for two-mode networks is level specific. A two-mode matrix X with dimensions g x h, where g is the number of level 1 nodes (e.g., medical doctors) and h is the number of level 2 nodes (i.e., hospitals). If the function is defined on the level 1 nodes, the density is computed as:

X^{g} = XX^{T}

D^{g} = \frac{\sum_{i = 1}^{g}\sum_{j = 1}^{g} x_{ij}^{g} }{g(g-1)}

In contrast, if it is defined on the level 2 nodes, the density is:

X^{h} = X^{T}X

D^{h} = \frac{\sum_{i = 1}^{h}\sum_{j = 1}^{h} x_{ij}^{h} }{h(h-1)}

Moreover, as discussed in Wasserman and Faust (1994: 316), the density can be based on the dichotomous relations instead of the shared membership values. This can be specified by binary = TRUE.

Value

The level-specific network density for the two-mode graph.

Author(s)

Kevin A. Carson kacarson@arizona.edu, Diego F. Leal dflc@arizona.edu

References

Wasserman, Stanley and Katherine Faust. 1994. Social Network Analysis: Methods and Applications. Cambridge University Press.

Knoke, David and Song Yang. 2020. Social Network Analysis. Sage: Quantitative Applications in the Social Sciences (154).

Examples

#Replicating the biparitate graph presented in Knoke and Yang (2020: 109)
knoke_yang_PC <- matrix(c(1,1,0,0, 1,1,0,0,
                          1,1,1,0, 0,0,1,1,
                          0,0,1,1), byrow = TRUE,
                          nrow = 5, ncol = 4)
colnames(knoke_yang_PC) <- c("Rubio-R","McConnell-R", "Reid-D", "Sanders-D")
rownames(knoke_yang_PC) <- c("UPS", "MS", "HD", "SEU", "ANA")
#compute two-mode density for level 1
#note: this value does not match that of Knoke and Yang (which we believe
#is a typo in that book), but does match that of Wasserman and
#Faust (1995: 317) for the ceo dataset.
computeTMDens(knoke_yang_PC, level1 = TRUE)
#compute two-mode density for level 2.
#note: this value matches that of the book
computeTMDens(knoke_yang_PC, level1 = FALSE)

dream documentation built on Aug. 8, 2025, 6:36 p.m.