  Group consensus implies reaching multiple convergence groups where agents
belonging to the same cluster converge. This paper focuses on linear
multi-agent systems under nonnegative directed graphs. A new necessary and
sufficient condition for ensuring group consensus is derived, which requires
the spanning forest of the underlying directed graph and that of its quotient
graph induced with respect to a clustering partition to contain equal minimum
number of directed trees. This condition is further shown to be equivalent to
containing cluster spanning trees, a commonly used topology for the underlying
graph in the literature. Under a designed controller gain, lower bound of the
overall coupling strength for achieving group consensus is specified. Moreover,
the pattern of the multiple synchronous states formed by all clusters is
characterized by setting the overall coupling strength be large enough.
