It is well known that under mild conditions any two local minima can be connected via an alternating sequence of local minima and index-1 saddle points. Starting from a system of ODEs whose fixed points are index-1 saddle points we propose a global optimisation algorithm. The algorithm constructs a graph of the local minima and saddle points of a differentiable function. Different strategies are proposed that enable the algorithm to escape from stationary points that are already in the graph.