<｜begin▁of▁sentence｜>### Instruction:
Imagine you're working on an interactive web visualization that represents a network infrastructure. As part of this project, you're implementing an algorithm to ensure network resilience. Currently, the visualization depicts a simplistic model of a network: a linear sequence of four interconnected nodes representing servers, with a fifth isolated server that's not yet integrated into the main network.

Your task is to enhance the network's reliability by achieving 2-edge connectivity. This means that every server in the network should have at least two independent paths to every other server. To accomplish this, you've been provided with a dataset detailing potential additional connections that could be established between servers, each with an associated cost (weight).

You need to determine which of the proposed connections (edges) from this dataset should be added to your network visualization to achieve 2-edge connectivity. It's important to select these connections judiciously, taking into consideration both the cost and the condition that every proposed edge is actually available for use.

How would you incorporate this logic into the backend to automatically update the network visualization with the optimal set of additional edges, ensuring the network is robust against a single connection failure while adhering to the constraints of edge availability and cost-effectiveness?
### Response:
import networkx as nx

# Create a path graph with an additional node
G = nx.path_graph((1, 2, 3, 4))
G.add_node(5)

# Available edges with weights
avail = {(1, 5): 11, (2, 5): 10, (4, 3): 1, (4, 5): 51}

# Find a set of edges that 2-edge-connects the graph G
augmentation = sorted(nx.k_edge_augmentation(G, k=2, avail=avail))

# Print the augmentation set
print(augmentation)
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