A random opinion formation model over signed networks

We study a random opinion dynamics model over signed networks with two different topological assumptions, that is, strongly connected and quasi-strongly connected. The model is proposed in a gossip algorithm form for simplicity but can be extended to a general one: at each time, a subgraph of the underlying interaction graph is selected and agents exchange their opinions based on this selected subgraph. It is shown that when the interacting graph is strongly connected, structurally balance is crucial for opinion clustering. However, when the interacting graph is quasi-strongly connected, the structurally balance assumption of the rooted graph is not enough for the convergence of the system and agents that are not roots may end in fluctuation.