Fig 1. Illustration of a successful greedy path on a network embedded in the 2D-plane (indicated by the grid; distances correspond to the length of the straight line between two nodes).

The corresponding topological and geometrical stretches are respectively 1.33 and approximatively 0.91, thus illustrating how geometrical stretch can be lower than 1. Notice that the shortest and the greedy paths would coincide if the role of the source and of the target were exchanged (i.e., seeking a greedy path from the red node to the blue one instead).