  Signed graphs have been introduced to enrich graph structures expressing
relationships between persons or general social entities, introducing edge
signs to reflect the nature of the relationship, e.g., friendship or enmity.
Independently, offensive alliances have been defined and studied for
undirected, unsigned graphs. We join both lines of research and define
offensive alliances in signed graphs, hence considering the nature of
relationships. Apart from some combinatorial results, mainly on k-balanced and
k-anti-balanced signed graphs (where the latter is a newly introduced family of
signed graphs), we focus on the algorithmic complexity of finding smallest
offensive alliances, looking at a number of parameterizations. While the
parameter solution size leads to an FPT result for unsigned graphs, we obtain
W[2]-completeness for the signed setting. We introduce new parameters for
signed graphs, e.g., distance to weakly balanced signed graphs, that could be
of independent interest. We show that these parameters yield FPT results. Here,
we make use of the recently introduced parameter neighborhood diversity for
signed graphs.
