Nonneighboring

Nonneighboring is an adjective meaning not neighboring or not adjacent. In general use it refers to elements that are separated by at least one intervening element, boundary, or connection. The term is common in discussions of spatial arrangements, graphs, grids, and networks, where proximity and adjacency carry specific meanings.

In graph theory, two vertices are nonneighboring if they are not connected by an edge. The concept is often used when describing neighborhoods, or when considering the complement graph, where nonneighboring pairs become edges. Distance between nonneighboring vertices is at least two. A simple example: in a path of three vertices, 1 and 3 are nonneighboring.

In spatial grids and cellular automata, a cell has a neighborhood consisting of adjacent cells. Nonneighboring cells lie outside this neighborhood and do not directly influence the cell in one step. For example, in a Moore neighborhood of radius 1, nonneighboring cells are those beyond the surrounding eight cells.

Other uses appear in chemistry, biology, and network analysis. In chemistry and biology, nonneighboring atoms or groups are those not bonded or not immediately adjacent along a chain. In social networks and geography, nonneighboring individuals or locations are not directly connected or contiguous but may be linked via intermediaries. The term serves as a descriptive contrast to neighboring or adjacent elements across disciplines.