For several decades graphs act as a powerful and flexible representation formalism in pattern recognition and related fields. For instance, graphs have been employed for specific tasks in image and video analysis, bioinformatics, or network analysis. Yet, graphs are only rarely used when it comes to handwriting recognition. One possible reason for this observation might be the increased complexity of many algorithmic procedures that take graphs, rather than feature vectors, as their input. However, with the rise of efficient graph kernels and fast approximative graph matching algorithms, graph-based handwriting representation could become a versatile alternative to traditional methods. This paper aims at making a seminal step towards promoting graphs in the field of handwriting recognition. In particular, we introduce a set of six different graph formalisms that can be employed to represent handwritten word images. The different graph representations for words, are analysed in a classification experiment (using a distance based classifier). The results of this word classifier provide a benchmark for further investigations.