contract p g will perform edge contraction on the graph g. The edges for which the property p holds/is true will get contracted: The resulting graph will not have these edges; the start- and end-node of these edges will get united. The result graph does not include nodes with no incoming or outgoing edges.

As for contract but additionally returns a mapping that associates each node in the original graph to the set of nodes with which it is contracted in the result graph. The minimum element of each such set is used as the representative of the set in the result graph. Nodes with no incoming or outgoing edges are present in the mapping even if they are omitted from the result graph.