<｜begin▁of▁sentence｜>### Instruction:
In the scenario where a Health Inspector is tasked with designing an efficient inspection route through a city's network of five interconnected clinics, with the clinics connected along the following pathways: Clinic 1 to Clinic 2, Clinic 2 to Clinic 3, Clinic 3 to Clinic 4, Clinic 4 to Clinic 5, and Clinic 5 back to Clinic 1. The challenge lies in determining the smallest set of pathways to cover such that every clinic is either directly inspected or is adjacent to an inspected clinic. How might one utilize NetworkX to identify this essential set of pathways to ensure the Health Inspector's route is as efficient as possible, thereby guaranteeing comprehensive inspection coverage with minimal redundancy?
### Response:
import networkx as nx

# Create a graph
G = nx.Graph()
G.add_edges_from([(1, 2), (2, 3), (3, 4), (4, 5), (5, 1)])

# Compute minimum edge dominating set
min_edge_dom_set = nx.min_edge_dominating_set(G)
print('Minimum edge dominating set:', min_edge_dom_set)
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