adjacents

Adjacents is a noun formed from the adjective adjacent, used to refer to items that lie next to each other within a defined arrangement or relationship. The term appears most often in technical writing to denote the set of neighboring elements around a given item. In common use, one can simply speak of adjacent items rather than adjacents.

In mathematics and computer science, adjacency is a formal relation. In a sequence, two elements are adjacent if they appear consecutively. In graph theory, two vertices are adjacent when they share an edge, and a vertex’s adjacents are its neighbors. Adjacency structures include adjacency matrices and adjacency lists that encode these relations. In grid-based models, adjacency defines which cells or pixels can interact, with common schemes such as four-neighborhood or eight-neighborhood.

In geography and spatial analysis, adjacents are regions that share a common boundary. Border relations influence political, economic, and environmental considerations, from map-making to resource management.

In other domains, adjacency influences data structures and algorithms, for example, in image processing where adjacent pixels form local patterns, or in sentence processing where adjacent words affect syntax and meaning. In discourse analysis, adjacent turns or responses may be examined for interaction patterns, though the term adjacency is more common than adjacents in formal prose.

Origins: from Latin adiacere, meaning lying near. The plural adjacents is used in some contexts to describe neighboring items, but many writers prefer phrases such as adjacent items, adjacent vertices, or adjacencies to indicate this relation.