Graph contraction is an operation that simplifies a graph by merging two adjacent vertices into a single vertex, effectively reducing the number of vertices while preserving the essential structure of the graph. This process not only impacts the vertex set but also alters the edges connected to the merged vertices, allowing for a clearer view of the graph's connectivity. The concept is crucial in both labeled and unlabeled graphs, as it helps analyze graph properties and explore equivalences among various configurations.
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