This document describes a new algorithm called GRAph ALigner (GRAAL) for topological network alignment. GRAAL aims to provide a unique global alignment of nodes between two networks based solely on topological similarity, without using other a priori information. It works by first finding a dense core between the networks to seed the alignment, then expanding outwards in spheres of increasing radius to align additional nodes. The alignment score is based on the percentage of edges from the first network that are correctly aligned to edges in the second network. The algorithm is tested on sample networks and achieves an edge correctness of 0.089.