  Complementarity is one of the main features underlying the interactions in
biological and biochemical systems. Inspired by those systems we propose a
model for the dynamical evolution of a system composed by agents that interact
due to their complementary attributes rather than their similarities. Each
agent is represented by a bit-string and has an activity associated to it; the
coupling among complementary peers depends on their activity. The connectivity
of the system changes in time respecting the constraint of complementarity. We
observe the formation of a network of active agents whose stability depends on
the rate at which activity diffuses in the system. The model exhibits a
non-equilibrium phase transition between the ordered phase, where a stable
network is generated, and a disordered phase characterized by the absence of
correlation among the agents. The ordered phase exhibits multi-modal
distributions of connectivity and activity, indicating a hierarchy of
interaction among different populations characterized by different degrees of
activity. This model may be used to study the hierarchy observed in social
organizations as well as in business and other networks.
