Description Usage Arguments Details Value Note Author(s) References See Also Examples

A function to construct semiring structures for the analysis of structural balance theory.

1 2 |

`x` |
an object of a ' |

`type` |
balance or 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 |

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 determinate 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.

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 |

Disabling transitive closure should be made with good substantial reasons.

Antonio Rivero Ostoic

Harary, F, Z. Norman, and D. Cartwright *Structural Models: An Introduction to the Theory of Directed Graphs*. New York: John Wiley & Sons. 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.

1 2 3 4 5 6 7 8 9 10 | ```
## 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
sg <- signed(arr)
## Establish the semiring structure
semiring(sg)
``` |

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