<｜begin▁of▁sentence｜>### Instruction:
Imagine a marine archaeologist delving into the intricate world of underwater social networks, grappling with the complex interactions that once thrived among the sailors of a sunken fleet. The aim is to map out these historical interactions, treating each individual as a submerged relic (node) and every exchange between them as the waters that connect them (weighted edges). To bring this submerged network to the surface in a way that reveals the closeness of relationships and the prominence of certain individuals within this aquatic society, the archaeologist seeks to employ the “layout_tsne” function from the graspologic toolkit. This advanced tool will help in reducing the vast ocean of social connections into a manageable 2D treasure map, where the proximity on the map mirrors the closeness of their interactions, and the size of each relic (node) signifies its significance amongst the fleet. How can the archaeologist use this “layout_tsne” function to not only chart these ancient social currents but also unearth the clusters of communities that once sailed the shared seas, ensuring that the visualization remains as truthful to the original network structure as possible?
### Response:
import networkx as nx
from graspologic.layouts import layout_tsne

# Step 1: Construct a social network graph with nodes and weighted edges
G = nx.Graph()
nodes = range(100)
edges = [(i, j, {'weight': np.random.rand()}) for i in nodes for j in nodes if i < j and np.random.rand() > 0.5]
G.add_nodes_from(nodes)
G.add_edges_from(edges)

# Step 2: Use t-SNE layout for dimensionality reduction
# Here we specify 'weight' attribute for edge weights and a random_seed for reproducibility
result = layout_tsne(G, perplexity=30, n_iter=1000, max_edges=10000000, weight_attribute='weight', random_seed=42, adjust_overlaps=True)

# Step 3: Access and print the positions
largest_cc, positions = result
for position in positions:
    print(f"Node {position.node_id}: x={position.x}, y={position.y}, size={position.size}, community={position.community}")
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