  This paper targets at exploring how to characterize collective behaviors of
directed signed networks. The right eigenvector of the Laplacian matrix
associated with zero eigenvalue is further investigated and its mathematical
expression is proposed. It is shown that the right eigenvector plays an
important role in determining the collective behaviors of directed signed
networks. Furthermore, algebraic criteria are introduced for collective
behaviors of directed signed networks, such as bipartite consensus, interval
bipartite consensus and bipartite containment tracking. In addition, a
simulation example is given to the correctness of our developed theoretical
results.
