Consensus protocols achieve an agreement among agents thanks to the collaborativ
e efforts of all agents, expresses by a (connected) communication graph with non
negative weights.
The question we ask in this paper is the following: is it possible to achieve a
form of agreement in presence of antagonistic interactions, modeled as negative
weights on the communication graph?
The answer to this question is affirmative: on signed networks all agents can co
nverge to a consensus value which is the same for all except for the sign.
Necessary and sufficient conditions are obtained to describe the cases when this
is possible.
