Relatiu

Relatiu is a theoretical construct used in the study of relational modeling and network theory. It denotes a quantitative measure of the strength or presence of a relation between two elements within a system. The term is etymologically derived from the Latin relatio and the suffix -tu, and is used in academic discussions to distinguish this measure from the mere existence of a connection.

Formal definition: Given a set of elements V, a Relatiu function R assigns a nonnegative value R(i,j) for each ordered pair (i,j) in V×V, representing the strength of the relation from i to j. In many implementations R(i,i)=0. Relatiu can be static, capturing a snapshot, or dynamic, incorporating time t → R_t(i,j). It is often derived from an underlying graph or matrix W with weights w_ij; a normalization step yields probabilities R_norm(i,j) = w_ij / sum_k w_ik.

Variants and computation: Variants include directional Relatiu (asymmetric) and symmetric Relatiu. Computation uses adjacency matrices, feature vectors, and temporal factors. Common forms are proportional allocations, exponentiated scores, or learned parameters in a model.

Applications: Used to model dependency or influence strengths in linguistic parsing, social networks, information flow, and cognitive simulations. It supports comparing relational configurations across subgraphs and time.

See also: Relational model, Graph theory, Tensor, Network science, Dependency grammar.