Just launched! Get 30% off Rails Revisited Have a Look

Graph Traversal: Bellman Ford

Buy or Subscribe

You can access this course in just a minute, and support my efforts to rid the world of crappy online courses!

Buy Standalone  Subscribe

One of the most fascinating uses of graphs is in the optimization of path traversal, which can be used in a vast number of calculations.

As mentioned in the previous chapter, graphs can be used to represent all kinds of information:

  • A network of any kind. Social (friends) or digital (computers or the internet), for example
  • A decision tree
  • Contributions from members of any kind to a cause of any kind
  • Atomic interactions in physics, chemistry or biology

Navigation between various endpoints - If you apply weighting to the edges or vertices, you can run useful calculations for just about anything. One of the most common is finding the shortest path between two vertices.

//Bellman-Ford: Shortest path calculation
//on an edge-weighted, directed graph
const vertices = ["S", "A", "B", "C", "D", "E"];
var memo = {
const graph = [
  {from : "S", to : "A", cost: 4},
  {from : "S", to :"E", cost: -5},
  {from : "A", to :"C", cost: 6},
  {from : "B", to :"A", cost: 3},
  {from : "C", to :"B", cost: -2},
  {from : "D", to :"C", cost: 3},
  {from : "D", to :"A", cost: 10},
  {from : "E", to: "D", cost: 8}

const iterate = () => {
  var doItAgain = false;
  for(fromVertex of vertices){
    const edges = graph.filter(path => {
      return path.from === fromVertex;
    for(edge of edges){
      const potentialCost = memo[edge.from] + edge.cost;
      if(potentialCost < memo[edge.to]){
        memo[edge.to] = potentialCost;
        doItAgain = true;
  return doItAgain;
for(vertex of vertices){
  if(!iterate()) break;