Cirkelfria

Cirkelfria is a Swedish term used to describe objects, processes, or structures that are free from circles or cycles. In mathematics and computer science, it denotes the absence of closed loops in a system, such as a graph or dependency structure. The word is formed from cirkel (circle) and fri (free).

In graph theory, a structure is cirkelfria if it contains no cycles. A directed acyclic graph (DAG) is a canonical example of a cirkelfri object: there is a topological ordering of its vertices and no path leads back to a previous vertex. In undirected graphs, being circle-free means the graph is a forest (a collection of trees) with no simple cycles. The concept is closely related to acyclicity and is central to ensuring well-defined evaluation orders and avoiding infinite loops.

Cycle-detection methods are routinely used to determine whether a given structure is cirkelfri. Depth-first search (DFS) can identify back edges that indicate cycles, while Kahn’s algorithm for topological sorting can verify acyclicity in directed graphs. In practical applications, cirkelfria structures are desirable because they enable predictable computation, stable dependencies, and clear execution orders.

Common domains where cirkelfria is relevant include software build systems and package management, where circular dependencies can cause failures, and spreadsheet design, where circular references lead to calculation issues. The English equivalents of the term are cycle-free or acyclic, with DAGs representing a prominent class of cirkelfria structures.

See also: acyclic graph, directed acyclic graph, forest, topological sort, cycle detection.