For a connected graph whose 2-core contains a vertex of degree at least three, suppress each maximal path with degree-two internal vertices to a single edge, allowing its two endpoints to coincide. The resulting multigraph, retaining loops and parallel edges, is its kernel. Suppression preserves graph excess and leaves minimum degree at least three. A purely cyclic core is a separate unicyclic case; it has no branching vertex to anchor this construction.
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A graph kernel is a method used in machine learning and pattern recognition that measures the similarity between two graphs. Graphs are data structures composed of nodes (or vertices) and edges connecting these nodes. They can represent various types of data, such as social networks, molecular structures, and more. Graph kernels are particularly useful for tasks involving graph-structured data, where traditional vector-based methods are not applicable.