Kohonen's Self-Organizing Map is a popular method which allows the projection of high dimensional data onto a low dimensional display space. Models of Self-Organizing Maps for the treatment of graphs have also been defined and studied. This paper proposes an extension to the GraphSOM model which substantially improves the stability of the model, and, as a side effect, allows for an acceleration of training. The proposed extension is based on a soft encoding of the information needed to represent the vertices of an input graph. Experimental results demonstrate the advantages of the proposed extension.