In a context where trees are supposed to have a root, a tree without any designated root is called a free tree. A free tree is an unrooted tree, defined to be a connected graph having no cycles and no size restrictions, the only constraint is to maintain the no loop nature of trees. If any edge of a free tree is deleted, the free tree ceases to exist, as it is no longer connected. In biology, unroot a tree has two possible scenarios: dead or rerooting. there are two ways to reroot plants: in water, and in a rooting medium such as soil. Depending on the plant it requires specific temperature or external chemical components to stimulate root growth.
*Used for example to analyzing networks or showing the structure of hydrocarbons, a graph with no loop & no root. http://pipelines.local/images/Hydrocarbons_800.gif