Judging the quality of handwriting based on visuo-structural criteria is fundamental for teachers when accompanying children who are learning to write. Automatic methods for quality assessment can support teachers when dealing with a large number of handwritings, in order to identify children who are having difficulties. In this paper, we investigate the potential of graph-based handwriting representation and graph matching to capture visuo-structural features and determine the legibility of cursive handwriting. On a comprehensive dataset of words written by children aged from 3 to 11 years, we compare the judgment of human experts with a graph-based analysis, both with respect to classification and clustering. The results are promising and highlight the potential of graph-based methods for handwriting evaluation.