Connections.rooted(x)
The operator "rooted" was introduced to improve efficiency: A tool that constructs the graph with the Connections.branch/.root etc. built-in operators has to cut the graph in order to arrive at "spanning trees". If there is a statement "Connections.branch(A,B)", then "rooted(A)" returns true, if "A" is closer to the root of the spanning tree as "B". Otherwise false is returned. For the MultiBody library this allows to avoid unnecessary small linear systems of equations.
OpenModelica, rooted(x) always returns true. See rooted ticket in the Modelica Trac for details.