<｜begin▁of▁sentence｜>### Instruction:
Given a graph built with the edges and nodes specified in the paths variable (where each tuple represents a path within the graph), how can one use the EdgeComponentAuxGraph in NetworkX to determine the k-edge-connected components for different values of k (in this case, k=1, k=2, k=3, and k=4)?
### Response:
import itertools as it
from networkx.utils import pairwise
from networkx.algorithms.connectivity import EdgeComponentAuxGraph

# Define a graph with multiple levels of k-edge-connected components
paths = [
    (1, 2, 3, 4, 1, 3, 4, 2),  # a 3-edge-connected component (a 4 clique)
    (5, 6, 7, 5),              # a 2-edge-connected component (a 3 clique)
    (1, 5),                    # combine the first two ccs into a 1-edge-connected component
    (0,),                      # add an additional disconnected 1-edge-connected component
]
G = nx.Graph()
G.add_nodes_from(it.chain(*paths))
G.add_edges_from(it.chain(*[pairwise(path) for path in paths]))

# Construct the auxiliary graph
aux_graph = EdgeComponentAuxGraph.construct(G)

# Query k-edge-connected components
components_k1 = sorted(map(sorted, aux_graph.k_edge_components(k=1)))
components_k2 = sorted(map(sorted, aux_graph.k_edge_components(k=2)))
components_k3 = sorted(map(sorted, aux_graph.k_edge_components(k=3)))
components_k4 = sorted(map(sorted, aux_graph.k_edge_components(k=4)))

# Output the components
print('1-edge-connected components:', components_k1)
print('2-edge-connected components:', components_k2)
print('3-edge-connected components:', components_k3)
print('4-edge-connected components:', components_k4)
<|EOT|>
