<｜begin▁of▁sentence｜>### Instruction:
Alrighty, as a pilot, you're quite familiar with the importance of being precise and following procedures to safely ferry passengers or cargo from one point to another. Similarly, when we handle data analysis or graph algorithms, we have specific tools and steps we need to follow to ensure the job is done correctly and efficiently.

So, picture this: you're in the cockpit, ready to chart a complex route based on weather, air traffic, and a myriad of other factors. Now, translate that into the world of graphs and networks. We have a network, which is akin to a map full of interconnected destinationsÃ¢ÂÂour nodes and edges.

In this scenario, our task is to extract a smaller section of our overall "flight map" to focus on a specific areaÃ¢ÂÂmuch like how youÃ¢ÂÂd zoom into a flight path between two cities. To do this, we have a tool similar to how youÃ¢ÂÂd use autopilot or a flight management system. This tool is the `RandomEdgeSamplerWithInduction` from the littleballoffur library, which is designed to sample a subsection of our complex network for an in-depth analysis.

Let's say our network is stored in a digital format ready for us to process. In our case, itÃ¢ÂÂs like having our flight map stored on an electronic flight bag. We have this graph recorded in a `.sparse6` file named `littleballoffur1.sparse6`.

What we want to do is to extract a smaller subset or "sample" of our network routes where we want to keep a specific number of connections (edges) between our waypoints (nodes). But hereÃ¢ÂÂs a crucial addition: just like how air traffic control might require keeping some indirect routes between certain cities due to airspace regulations, we want to keep all the direct connections between waypoints we've already included in our sample. This method ensures that if two waypoints are selected, every direct route between them in the original network also remains in our sample, maintaining the integrity and connectivity of our selected area.

So, Captain, your mission, should you choose to accept it, is this: using the `RandomEdgeSamplerWithInduction` function from littleballoffur, how would you sample a subgraph from `littleballoffur1.sparse6` with a predetermined number of connections, while ensuring that you retain all direct connections (edges) between the waypoints (nodes) that make it into your sample? If the information was stored in a `.gml` file instead, youÃ¢ÂÂd be looking for the `littleballoffur1.gml` to perform the same operation.

I'm here to guide you through this process, but I trust that with your attention to detail and step-by-step methodology, you'll be navigating through the network airspace with the same confidence you show when flying through the skies!
### Response:
import networkx as nx
from littleballoffur import RandomEdgeSamplerWithInduction
G = nx.read_sparse6('littleballoffur1.sparse6')
sampler = RandomEdgeSamplerWithInduction(number_of_edges=10, seed=42)
sampler_G = sampler.sample(G);
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