Как сделать взвешенный график из словаря?

Предполагая, что G - ваш график:

graph = {}

graph["A"] = {}
graph["A"] ["B"] = 1 
graph["A"] ["C"] = 3 
graph["A"] ["D"] = 2 

graph["B"] = {} 
graph["B"] ["D"] = 7
graph["B"] ["F"] = 5

graph["C"] = {}
graph["C"] ["E"] = 5

graph["D"] = {}
graph["D"] ["B"] = 7
graph["D"] ["E"] = 1

graph["E"] = {}
graph["E"] ["F"] = 4

graph["F"] = {}

for k,v in graph.items():
    for l, w in v.items():
        print(k, l, w)
        G.add_edge(k,l, weight=w)

Документация

На вашем примере graph. Объедините ключи в graph с каждым элементом в его значении. Используйте .add_weighted_edges_from, чтобы добавить ребра.

import networkx as nx
G = nx.Graph()

for k, v in graph.items():
    edges = [(k,b,w) for b,w in v.items()]
    print(edges)
    #G.add_weighted_edges_from(edges)
    G.add_weighted_edges_from((k,b,w) for b,w in v.items())

>>>
[('A', 'B', 1), ('A', 'C', 3), ('A', 'D', 2)]
[('B', 'D', 7), ('B', 'F', 5)]
[('C', 'E', 5)]
[('D', 'B', 7), ('D', 'E', 1)]
[('E', 'F', 4)]
[]

---
>>> for edge in G.edges.data():
...     print(edge)
('A', 'B', {'weight': 1})
('A', 'C', {'weight': 3})
('A', 'D', {'weight': 2})
('B', 'D', {'weight': 7})
('B', 'F', {'weight': 5})
('C', 'E', {'weight': 5})
('D', 'E', {'weight': 1})
('F', 'E', {'weight': 4})