<｜begin▁of▁sentence｜>### Instruction:
Given a graph with the edge set [('A', 'B', 2), ('B', 'C', 3), ('C', 'D', 4), ('C', 'E', 5), ('D', 'E', 6)], with the weight of each node initially set to its degree, compute the approximate minimum weighted dominating set using NetworkX.
### Response:
import networkx as nx

# Create a weighted graph
G = nx.Graph()
G.add_edge('A', 'B', weight=2)
G.add_edge('B', 'C', weight=3)
G.add_edge('C', 'D', weight=4)
G.add_edge('C', 'E', weight=5)
G.add_edge('D', 'E', weight=6)

# Node weights can be any numerical attribute
for node in G.nodes():
    G.nodes[node]['weight'] = G.degree[node]

# Find the approximate minimum weighted dominating set
approx_dom_set = nx.algorithms.approximation.min_weighted_dominating_set(G, weight='weight')

print('Approximate minimum weighted dominating set:', approx_dom_set)
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