<｜begin▁of▁sentence｜>### Instruction:
As a court reporter, I'm more familiar with capturing every word said in a courtroom verbatim, ensuring the legal transcripts reflect the proceedings with pinpoint accuracy. Just as attorneys meticulously examine evidence to build a case, I'll meticulously detail out the steps for working with graph data, meticulously ensuring every detail is noted for accuracy. ItÃ¢ÂÂs like when the court asks for a specific case file; I need to sift through our records to extract the pertinent information accurately Ã¢ÂÂ in this scenario; we're dealing with a digital Ã¢ÂÂcase fileÃ¢ÂÂ of sorts.

Within this context, let's take our scenario into the realm of network analysis. I've got this fascinating case file, let's call it "littleballoffur8.sparse6," not unlike the case numbers we handle here. Now, my job is to extract a subset of this network - a connected "testimony" of nodes, if you will. The goal is to pick out a subgraph, specifically one with 10 nodes, similar to how IÃ¢ÂÂd isolate a 10-page transcript from a day-long deposition.

However, just as a judge might set specific conditions for admitting evidence, we need to apply a certain rule when we're selecting our subset - think of it like a legal constraint on the process. We're going to use the MetropolisHastingsRandomWalkSampler with a little twist; we introduce what is known as a 'rejection constraint' with an exponent of 0.5. It's like being extra cautious about what testimony is permitted.

Translating this to our "legal-ease", I'd say: Could you demonstrate how to use MetropolisHastingsRandomWalkSampler to extract a specific, connected part of our digital case file Ã¢ÂÂ "littleballoffur8.sparse6" Ã¢ÂÂ ensuring we follow the "rule of 0.5" to precisely retrieve a segment of our network that encapsulates exactly 10 nodes? Remember, we need to maintain connectivity, as if ensuring all witnessesÃ¢ÂÂ testimonies are related to the case at hand. If this were a gml file, we'd nominate it the official file name for our records.
### Response:
import networkx as nx
from littleballoffur import MetropolisHastingsRandomWalkSampler
G = nx.read_sparse6('littleballoffur8.sparse6')
sampler = MetropolisHastingsRandomWalkSampler(number_of_nodes=10, seed=42, alpha=0.5)
sampled_graph = sampler.sample(G)
print(sampled_graph.edges(), sampled_graph.nodes())
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