  We tackle the problem of graph transformation with a particular focus on node
cloning. We propose a new approach to graph rewriting where nodes can be cloned
zero, one or more times. A node can be cloned together with all its incident
edges, with only its outgoing edges, with only its incoming edges or with none
of its incident edges. We thus subsume previous works such as the
sesqui-pushout, the heterogeneous pushout and the adaptive star grammars
approaches. A rewrite rule is defined as a span where the right-hand and
left-hand sides are graphs while the interface is a polarized graph. A
polarized graph is a graph endowed with some annotations on nodes. The way a
node is cloned is indicated by its polarization annotation. We use these
annotations for designing graph transformation with polarized cloning. We show
how a clone of a node can be built according to the different possible
polarizations and define a rewrite step as a final pullback complement followed
by a pushout. This is called the polarized sesqui-pushout approach. We also
provide an algorithmic presentation of the proposed graph transformation with
polarized cloning.
