<｜begin▁of▁sentence｜>### Instruction:
Imagine that you are delving into a family's lineage, tracing the connections from ancestor to descendant through the generations. You've come across a set of pivotal relationships that can be represented as connections following one from another: (1 to 2), (2 to 3), and (3 back to 1). To comprehend the full spectrum of family ties over time, you aspire to craft a comprehensive chart that not only shows these direct links but also illuminates all implied relationships within this bloodline, without redundantly noting an individual's connection to themselves.

Can you expand on this genealogical network and produce a refined pedigree chart that illustrates the whole expanse of relationships? It should encapsulate all indirect lineage linkages across this family tree, showcasing how each member is connected through various generations. It's paramount that in constructing this nexus, we avoid the superfluous step of denoting a person as their own ancestor, thus steering clear of needless self-associations. How might you achieve this using NetworkX, adhering to the significance and structure of the original connections among these family members?
### Response:
import networkx as nx

# Create a directed graph
DG = nx.DiGraph([(1, 2), (2, 3), (3, 1)])

# Generate the transitive closure of the graph
TC = nx.transitive_closure(DG, reflexive=False)

# Print the edges of the transitive closure
print(TC.edges())

# Expected output:
# OutEdgeView([(1, 2), (1, 3), (1, 1), (2, 3), (2, 1), (2, 2), (3, 1), (3, 2), (3, 3)])
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