Python implementation of Dijkstra's Algorithm

gistfile1.py

class Graph:
  def __init__(self):
    self.nodes = set()
    self.edges = defaultdict(list)
    self.distances = {}

  def add_node(self, value):
    self.nodes.add(value)

  def add_edge(self, from_node, to_node, distance):
    self.edges[from_node].append(to_node)
    self.edges[to_node].append(from_node)
    self.distances[(from_node, to_node)] = distance


def dijsktra(graph, initial):
  visited = {initial: 0}
  path = {}

  nodes = set(graph.nodes)

  while nodes: 
    min_node = None
    for node in nodes:
      if node in visited:
        if min_node is None:
          min_node = node
        elif visited[node] < visited[min_node]:
          min_node = node

    if min_node is None:
      break

    nodes.remove(min_node)
    current_weight = visited[min_node]

    for edge in graph.edges[min_node]:
      weight = current_weight + graph.distance[(min_node, edge)]
      if edge not in visited or weight < visited[edge]:
        visited[edge] = weight
        path[edge] = min_node

  return visited, path

I am looking for an "opposite" of this. Something that finds the longest path between vertices.

Should you also have a line like this in the code below line 13? :
self.distances[(to_node, from_node)] = distance

@joyrexus your link is broken. Do you have a current link to an algorithm with O(m log n)?

This looks great, thank you. Can anyone tell me how to pass the values and get it to work? I'd like to demonstrate this to a class and am unsure on how to do this. Any comments or examples would be much appreciated.

all right but i watch a error in incomplete graph.

g = Graph()
g.add_node('x')
g.add_node('y')
g.add_node('z')
g.add_edge('x', 'y', 100)
g.add_edge('y', 'z', 90)
g.add_edge('z', 'x', 78)

print(dijsktra(g, 'x')) .... error
weight = current_weight + graph.distances[(min_node, edge)]
KeyError: ('x', 'z')

not exist conection to x::z

i change this lines

for edge in graph.edges[min_node]:
  try:
      weight = current_weight + graph.distances[(min_node, edge)]
  except:
      weight = current_weight + math.inf

  if edge not in visited or weight < visited[edge]:
    visited[edge] = weight
    path[edge] = min_node

I implemented it here as:

def dijkstra(graph, source):
    q = set()
    dist = {}
    prev = {}

    for v in graph.nodes:       # initialization
        dist[v] = INFINITY      # unknown distance from source to v
        prev[v] = INFINITY      # previous node in optimal path from source
        q.add(v)                # all nodes initially in q (unvisited nodes)

    # distance from source to source
    dist[source] = 0

    while q:
        # node with the least distance selected first
        u = min_dist(q, dist)

        q.remove(u)

        if u.label in graph.edges:
            for _, v in graph.edges[u.label].items():
                alt = dist[u] + v.length
                if alt < dist[v.to_node]:
                    # a shorter path to v has been found
                    dist[v.to_node] = alt
                    prev[v.to_node] = u

    return dist, prev

...with the objects:

class Node:
    def __init__(self, label):
        self.label = label

class Edge:
    def __init__(self, to_node, length):
        self.to_node = to_node
        self.length = length

class Graph:
    def __init__(self):
        self.nodes = set()
        self.edges = dict()

    def add_node(self, node):
        self.nodes.add(node)

    def add_edge(self, from_node, to_node, length):
        edge = Edge(to_node, length)
        if from_node.label in self.edges:
            from_node_edges = self.edges[from_node.label]
        else:
            self.edges[from_node.label] = dict()
            from_node_edges = self.edges[from_node.label]
        from_node_edges[to_node.label] = edge

There is a typo here "def dijsktra(graph, initial):". It would be better to change it as dijkstra.

I envy all the people here who can work on this code with no no problem and even if important info is missing! Well, 1) I miss info on where is 'graph' defined (or at least how to create one) and 2) I get "NameError: global name 'defaultdict' is not defined". Any ideas?

@AlkisPis, from collections import defaultdict to clear that error

@JeevaTM, Thanks. You are really very fast ... You replied on Feb 18 to a question I posted on Dec 18! :)) Well, except if you can see the future! :)

This follows the wikipedia definition closely:

http://rebrained.com/?p=392

import sys
def shortestpath(graph,start,end,visited=[],distances={},predecessors={}):
"""Find the shortest path btw start & end nodes in a graph"""

# detect if first time through, set current distance to zero
if not visited: distances[start]=0

# if we've found our end node, find the path to it, and return
if start==end:
    path=[]
    while end != None:
        path.append(end)
        end=predecessors.get(end,None)
    return distances[start], path[::-1]

# process neighbors as per algorithm, keep track of predecessors
for neighbor in graph[start]:
    if neighbor not in visited:
        neighbordist = distances.get(neighbor,sys.maxint)
        tentativedist = distances[start] + graph[start][neighbor]
        if tentativedist < neighbordist:
            distances[neighbor] = tentativedist
            predecessors[neighbor]=start

# neighbors processed, now mark the current node as visited 
visited.append(start)

# finds the closest unvisited node to the start 
unvisiteds = dict((k, distances.get(k,sys.maxint)) for k in graph if k not in visited)
closestnode = min(unvisiteds, key=unvisiteds.get)

# now take the closest node and recurse, making it current 
return shortestpath(graph,closestnode,end,visited,distances,predecessors)

if name == "main":
graph = {'a': {'w': 14, 'x': 7, 'y': 9},
'b': {'w': 9, 'z': 6},
'w': {'a': 14, 'b': 9, 'y': 2},
'x': {'a': 7, 'y': 10, 'z': 15},
'y': {'a': 9, 'w': 2, 'x': 10, 'z': 11},
'z': {'b': 6, 'x': 15, 'y': 11}}
print shortestpath(graph,'a','a')
print shortestpath(graph,'a','b')

"""
Expected Result:
    (0, ['a']) 
    (20, ['a', 'y', 'w', 'b'])
    """

I think you also need:

 self.distances[(to_node, from_node)] = distance

at line 14. Or else the algorithm won't know the distance from nodes A to B is the same as from B to A.

I think it's possible B to A is not the same as A to B. (For example, in a representation of a road network, a 1-way road). I think the user is responsible for adding B to A with the same distance in the usage of add_edge().
You can implement validation/setting that B to A is == A to B, but it would restrict your implementation to solely equidistant and single edge graphs. Would you agree?

I am not able to understand what to pass in the second argument (initial) for dijsktra function. Can anyone please help me?

it is the starting node which has no parent that's why 0