<｜begin▁of▁sentence｜>### Instruction:
In the context of assessing and optimizing the current network infrastructure within our organization's information system, we've been tasked to scrutinize an established communication graph composed of nodes representing departments and edges depicting direct communication lines between them. The graph's initial connections include pairs such as ('A', 'B'), ('A', 'C'), ('B', 'C'), ('C', 'D'), and ('D', 'E').

Our objective is to integrate a newly proposed direct line ('A', 'D'), enhancing the efficiency of the inter-departmental communication network. Following this update, it is crucial to reassess the communication efficiency of each department within the network, formally known as the closeness centrality, using NetworkX analysis tools.

We must ascertain an effective method to recalibrate the closeness centrality metrics for our nodes that accurately reflects the additional edge. This recalibration would provide us with valuable insights into the impact of the new communication line on the overall velocity and directness of information flow within our company's network infrastructure.

How can we, as systems analysts, formulate and execute an efficacious strategy for recalculating the closeness centrality measures leveraging NetworkX capabilities, upon the incorporation of the new edge ('A', 'D')? The intention is to achieve this without overhauling the entire network analysis since only a single connection has been established, thereby ensuring efficiency in our systems update process.
### Response:
import networkx as nx
from networkx.algorithms.centrality import incremental_closeness_centrality

# Create a graph
G = nx.Graph()
G.add_edges_from([('A', 'B'), ('A', 'C'), ('B', 'C'), ('C', 'D'), ('D', 'E')])

# Initial computation of closeness centrality before any edge modifications
initial_cc = nx.closeness_centrality(G)

# Add a new edge and update closeness centrality
G.add_edge('A', 'D')
updated_cc = incremental_closeness_centrality(G, ('A', 'D'), initial_cc)

print(updated_cc)
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