Combine edges when node degree is n in networkx

Question

I have an undirected graph as follows:

import networkx as nx
import matplotlib.pyplot as plt

l = [('1','2'),('2','3'),('3','4'),('3','5'),('1','6'),('6','7'),('6','8'),('9','8')]

G=nx.Graph()
G.add_edges_from(l)
nx.draw_networkx(G,with_labels=True)
plt.show()

I want to combine edges when node satisfies degree=n(like 2). I need remove node 1,2 and 8,and connect 3-6 and 6-9 in my example. So I expect the results to be as follows.

How can I do it? Thanks in advaence

Answer 1

import networkx as nx
import matplotlib.pyplot as plt

l = [('1','2'),('2','3'),('3','4'),('3','5'),('1','6'),('6','7'),('6','8'),('9','8')]

G=nx.Graph()
G.add_edges_from(l)

# Select all nodes with only 2 neighbors
nodes_to_remove = [n for n in G.nodes if len(list(G.neighbors(n))) == 2]

# For each of those nodes
for node in nodes_to_remove:
    # We add an edge between neighbors (len == 2 so it is correct)
    G.add_edge(*G.neighbors(node))
    # And delete the node
    G.remove_node(node)

nx.draw(G,with_labels=True)