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A function to construct semiring structures for the analysis of Structural Balance theory.
semiring(x, type = c("balance", "cluster"), symclos = TRUE,
transclos = TRUE, k = 2, lbs)An object of ‘Semiring’ class.
The items included are:
the valences in the semiring
the original semiring structure
the resulted semiring structure
the number of cycles or semicycles
an object of a ‘Signed’ class
balance for a balance semiring (default)
cluster for a cluster semiring
(logical) apply symmetric closure?
(logical) apply transitive closure?
length of the cycle or the semicycle
(optional) labels for the semiring output
Antonio Rivero Ostoic
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.
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.
signed, as.signed
# 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()
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