unrooted

Unrooted is an adjective describing something that lacks a fixed reference point or origin, typically a root. In mathematics and computer science, an unrooted structure is one without a designated root node or starting point. In biology, particularly phylogenetics, an unrooted tree is a tree that depicts relationships without prescribing a direction of evolution.

Rooted vs unrooted: A rooted tree has a distinguished vertex called the root from which all edges and nodes can be considered to descend. This introduces directionality or temporal order. An unrooted tree does not indicate an ancestral direction; it specifies which taxa are related but not which is ancestral to others.

In phylogenetics, unrooted trees summarize observed similarities (e.g., genetic distances) without assuming a common ancestor at a specific point in time. To interpret evolution over time, researchers root the tree, for example by including an outgroup, or by midpoint rooting which places the root on the middle of the longest path.

In graph theory, an unrooted tree is a connected acyclic graph without a root. It is sometimes called a free tree. Distances along the tree are symmetric and there is no natural starting point.

The concept is widely used in biology and computer science to represent relationships or hierarchical structures when a fixed origin is unknown or unnecessary.