NetworkX (Python): how to change edges' weight by designated rule

Question

I have a weighted graph:

F=nx.path_graph(10)
G=nx.Graph()
for (u, v) in F.edges():
    G.add_edge(u,v,weight=1)

get the nodes list:

[(0, 1), (1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (6, 7), (7, 8), (8, 9)]

I want to change each edge's weight by this rule:

remove one node, such as node 5, clearly, edge (4, 5) and (5, 6) will be delete, and the weight of each edge will turn to:

{# these edges are nearby the deleted edge (4, 5) and (5, 6)

(3,4):'weight'=1.1,

(6,7):'weight'=1.1,

#these edges are nearby the edges above mentioned

(2,3):'weight'=1.2,

(7,8):'weight'=1.2,

#these edges are nearby the edges above mentioned

(1,2):'weight'=1.3,

(8,9):'weight'=1.3,

# this edge is nearby (1,2)

(0,1):'weight'=1.4}

How to write this algorithm?

PS: path_graph is just an example. I need a program suit any graph type. Furthermore, the program need to be iterable, it means I can remove one node from origin graph each time.

Regards