Understanding the conditions under which a multiagent system reaches a consensus has wide applicability in distributed decision-making environments. The iterative exchange of local states (or opinions) between agents must usually adhere to various constraints. For example, an agent may update its state only from neighboring agents whose state does not differ by more than the agent's bound of confidence (BoC). In this paper, a novel method for generating an Erdos-Rényi random network that guarantees a consensus in a multi-agent system subject to agents' BoC constraints is presented. For the case when agents maintain binary uniformly distributed states, we provide theoretical results on the sensitivity of the network structure generated with respect to changes in the agent BoCs. To allow for more general types of uncertainty to be captured in agent states and the state update scheme, a Dempster-Shafer (DS) belief theoretic opinion model along with a non-parametric kernel density estimation method is utilized and the results are illustrated via a simulation. The method presented has numerous applications in social networks, autonomous mobile robots, distributed sensor systems, and viral marketing, to name a few. Furthermore, the model can be utilized to generate fault-tolerant multi-agent systems where the random network generation makes it difficult to fragment the agents via pre-planned attacks. A case study on autonomous robot soldiers is used for an illustration of these ideas.