  Originally, protocols were designed for multi-agent systems (MAS) using
information about the network. However, in many cases there is no or only
limited information available about the network. Recently, there has been a
focus on scale-free synchronization of multi-agent systems (MAS). In this case,
the protocol is designed without any prior information about the network. As
long as the network contains a directed spanning tree, the scale-free protocol
guarantees that the network achieves synchronization.
  If there is no directed spanning tree for the network then synchronization
cannot be achieved. But what happens when these scale-free protocols are
applied to such a network where the directed spanning tree no longer exists?
The latter might arise if, for instance, a fault occurs in one of more crucial
links. This paper establishes that the network decomposes into a number of
basic bicomponents which achieves synchronization among all nodes in this basic
bicomponent. On the other hand, nodes which are not part of any basic
bicomponent converge to a weighted average of the synchronized trajectories of
the basic bicomponents. The weights are independent of the initial conditions
and are independent of the designed protocol.
