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Merge selectionMerges the vertices that are currently selected. This means that all the selected vertices are replaced with one vertex that is connect with all the vertices that were connected with one of the selected vertices.
Split selectionSplits the vertices that are currently selected. This means that a vertex is split in to a number of vertices: one for each edge that arrives in that vertex.
Connect selectionConnects the vertices that are currently selected. This means that they become a clique.

Vertex induced graphReplaces the graph with the subgraph induced by the selected vertices. This graph contains only the vertices that are selected and the edges of which both endpoints are selected.
Edge induced graphReplaces the graph with the subgraph induced by the selected edges. This graph contains only the edges that are selected and the vertices that are the endpoints of these edges.

ComplementReplaces the current graph with its complement.
ClosureConstructs the closure of the current graph.
Line graphConstructs the line graph of the current graph.

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