adjacentness

Adjacentness is the property of being adjacent, meaning immediately next to or touching each other within a given framework. The term is used across disciplines to describe a close spatial or relational proximity without implying overlap.

In geometry and topology, two regions or figures are considered adjacent when they share a common boundary and have disjoint interiors. For example, two polygons in a planar tessellation that touch along an edge are adjacent. Definitions may distinguish edge-adjacent from vertex-adjacent, depending on whether sharing a boundary edge or only a corner suffices for adjacency.

In graph theory, adjacency describes the relation between vertices connected by an edge. If vertices u and v are adjacent, there is an edge {u, v}. The adjacency relation is symmetric in undirected graphs and is commonly represented with an adjacency matrix or adjacency lists. It is not generally reflexive in simple graphs.

In geographic information systems and spatial analysis, adjacentness describes neighboring polygons that share a boundary. Adjacency can be defined in terms of shared boundary length or area, and some contexts distinguish sharing an edge from sharing only a point.

In computer science and image processing, adjacency defines pixel or cell neighborhoods. Common schemes include 4-connectivity (sharing a side) and 8-connectivity (sharing a side or corner), which influence tasks such as region growing, contour finding, and object labeling.

Adjacency and adjacentness are therefore context-dependent terms that capture immediate proximity or direct connection within a structure. See also adjacency matrix, neighbor, and boundary.