zusammenhängige

Zusammenhängige is a German adjective meaning coherent, contiguous, or connected. It is used to describe things that form a unified whole, either spatially, structurally, or logically. In German grammar it is declined according to gender, number, and case (for example: zusammenhängende Menge, zusammenhängende Erzählung, die zusammenhängigen Teile).

In mathematics and related disciplines, zusammenhängig denotes connectedness. A zusammenhängige Menge is a connected set in topology: it cannot be split into two nonempty disjoint open subsets. A graph is called zusammenhängend or connected if there is a path between every pair of vertices; the term also appears in phrases like zusammenhängende Komponenten and zusammenhängende Teilmengen. The noun forms associated with the concept are Zusammenhängigkeit or Zusammenhang, depending on nuance.

In linguistic and literary contexts, zusammenhängige describes coherence and unity in text or discourse. A zusammenhängiger Text or eine zusammenhängende Erzählung has a clear structure, logical progression, and referential continuity between sentences and paragraphs, as opposed to fragmented or disjointed writing.

Etymology and grammar: the word is formed from zusammen- (together) and hängig (from hängen), conveying the idea of “hanging together.” It functions as a standard German adjective and is declined like other adjectives; endings vary with gender, number, and case, for example die zusammenhängigen Teile, ein zusammenhängender Text.

See also: connectedness, coherence, connected component, topology, graph theory.