Before revision:  In this document, we study the SCFE problem in real trees (also known as \mathbb{R show that a complete signed graph has a valid distance drawing in a real tree if  and only if  its subgraph composed of all (and only) its positive edges is strongly chordal . Furthermore, as an instrumental result, we show that the set of strongly chordal graphs is equal to the set of graphs with an intersection model of unit balls, proper balls, and balls in a real tree .
After revision:  In this document, we study the SCFE problem in real trees (also known as \mathbb{R show that a complete signed graph has a valid distance drawing in a real tree if and only if its subgraph composed of all (and only) its positive edges is strongly chordal .