WeightedGraph.py

from collections import defaultdict
import heapq

counter_steps = 0


def create_spanning_tree(graph, starting_vertex):
    global counter_steps
    mst = defaultdict(set)
    visited = set([starting_vertex])
    edges = [
        (cost, starting_vertex, to)
        for to, cost in graph[starting_vertex].items()
    ]
    heapq.heapify(edges)

    while edges:
        cost, frm, to = heapq.heappop(edges)
        if to not in visited:
            counter_steps += 1
            visited.add(to)
            mst[frm].add(to)
            for to_next, cost in graph[to].items():
                if to_next not in visited:
                    heapq.heappush(edges, (cost, to, to_next))

    return mst


example_graph = {
    'A': {'B': 2, 'C': 3},
    'B': {'A': 2, 'C': 1, 'D': 1, 'E': 4},
    'C': {'A': 3, 'B': 1, 'F': 5},
    'D': {'B': 1, 'E': 1},
    'E': {'B': 4, 'D': 1, 'F': 1},
    'F': {'C': 5, 'E': 1, 'G': 1},
    'G': {'F': 1},
}

print(create_spanning_tree(example_graph, 'A'))
print(counter_steps)