We present a graphical representation for palm vein patterns for use as biometric identifiers. The palm vein image captured from an infra red camera is converted into a spatial graph. After image enhancement and binarisation, the palm vein features are extracted from the skeleton using a novel two stage spur removal technique. The location of the features and the connections between them are used to define a Palm Vein Graph. Palm vein graphs are compared using the Biometric Graph Matching (BGM) Algorithm. We propose a graph registration algorithm that improves over existing state of the art algorithms for graph registration. We introduce 10 graph topology-based measures for comparing palm vein graphs. Experiments are conducted on a public palm vein database. One of the introduced measures, an edge-based similarity, gave a definite improvement in matching accuracies over other published results on the same database, especially for samples with only a small common overlap area due to displacement. In addition, when the edge-based measure was combined with one of three other topological features, we demonstrate a further improvement in matching accuracy.