A split link admits an embedded sphere in its complement with nonempty portions of the link on both sides. A split diagram admits a simple closed curve in the projection sphere separating nonempty portions of the diagram. A split diagram always represents a split link; the converse need not hold for an arbitrary diagram.
A split diagram has two nonempty parts separated by a simple closed curve disjoint from the diagram. For a two-component link, this is equivalent to disconnectedness of its projection graph. An alternating link diagram representing a split link cannot have a connected projection graph, as its Jones value at minus one detects a nonzero spanning-tree count.
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