semiring: Semiring Structures for Balance Theory

In multiplex: Algebraic Tools for the Analysis of Multiple Social Networks

Semiring Structures for Balance Theory

Description

A function to construct semiring structures for the analysis of Structural Balance theory.

Usage

semiring(x, type = c("balance", "cluster"), symclos = TRUE,
         transclos = TRUE, k = 2, lbs)

Arguments

x	an object of a ‘Signed’ class
type	balance for a balance semiring (default) cluster for a cluster semiring
symclos	(logical) apply symmetric closure?
transclos	(logical) apply transitive closure?
k	length of the cycle or the semicycle
lbs	(optional) labels for the semiring output

Details

Semiring structures are based on signed networks, and this function provides the capabilities to handle either the balance semiring or the cluster semiring within the Structural Balance theory.

A semiring combines two different kinds of operations with a single underlying set, and it can be seen as an abstract semigroup with identity under multiplication and a commutative monoid under addition. Semirings are useful to determine whether a given signed network is balanced or clusterable. The symmetric closure evaluates this by looking at semicycles in the system; otherwise, the evaluation is through closed paths.

Value

An object of ‘Semiring’ class. The items included are:

val	the valences in the semiring
s	the original semiring structure
Q	the resulted semiring structure
k	the number of cycles or semicycles

Note

Disabling transitive closure should be made with good substantial reasons.

Author(s)

Antonio Rivero Ostoic

References

Harary, F, Z. Norman, and D. Cartwright Structural Models: An Introduction to the Theory of Directed Graphs. Wiley. 1965.

Doreian, P., V. Batagelj and A. Ferligoj Generalized Blockmodeling. Cambridge University Press. 2004.

Ostoic, J.A.R. “Creating context for social influence processes in multiplex networks.” Network Science, 5(1), 1-29.

See Also

signed, as.signed

Examples

# create the data: two sets with a pair of binary relations 
# among three elements
arr <- round( replace( array( runif(18), c(3 ,3, 2) ), array( runif(18),
       c(3, 3, 2) ) > .5, 3 ) )

# make the signed matrix with two types of relations
# and establish the semiring structure
signed(arr) |> 
  semiring()

multiplex documentation built on Sept. 30, 2024, 5:07 p.m.