I'm solving a network optimization problem which is modeled as a graph $G=(V,E)$. Solving this problem using Pulp and NetworkX in Python and ordering the graph's nodes in a certain order (i.e. (1,2,3,4,5)) gives a certain optimal solution. However, changing the order of the nodes (i.e.,(3,4,1,2,5)) may lead to another optimal solution. Is there a metric for nodes that can order the nodes to provide the best optimal solution/s instead of going through the whole possible orders?