Existing results in the literature guarantee that the state of multi-agent systems interacting over networks that satisfy the cut-balance assumption asymptotically converges to a constant vector. Furthermore, when the network is persistently connected the agents reach a common value called consensus. Many real large-scale networks are obtained by sparsely connecting subnetworks of densely connected agents. In this context, our objective is to provide new cut-balance assumptions that are adapted to networks of clusters. They are useful for consensus and agreement in clusters in situations when network topology is such that clusters are given or can be easily identified. In this case our new cut-balance assumptions can be checked by realizing a smaller number of operations.