We introduce the concept of community consensus in the presence of malicious agents using a well-known median-based consensus algorithm. We consider networks that have multiple well-connected regions that we term communities, characterized by specific robustness and minimum degree properties. Prior work derives conditions on properties that are necessary and sufficient for achieving global consensus in a network. This however, requires the minimum degree of the network graph to be proportional to the number of malicious agents in the network, which is not very practical in large networks. In this work we present a natural generalization of this previous result. We characterize cases when although global consensus is not reached, some subsets of agents $V_i$ will still converge to the same values $\mathcal{M}_i$ among themselves. We define more relaxed requirements for this new type of consensus to be reached in terms of the number $k$ of edges connecting an agent in a community to agents external to the community, and the number of malicious agents in each community.

翻译：我们引入了一种在存在恶意代理的情况下基于广泛使用的中值共识算法实现社区共识的概念。我们考虑具有多个高度连通区域（称为社区）的网络，这些区域以特定的鲁棒性和最小度性质为特征。先前的研究推导了实现网络全局共识所必需且充分的条件属性。然而，这要求网络图的最小度与网络中恶意代理的数量成比例，这在大型网络中并不实用。在本文中，我们对这一先前结果进行了自然推广。我们刻画了当全局共识未达成时，某些代理子集 $V_i$ 仍会在其内部收敛到相同值 $\mathcal{M}_i$ 的情况。我们针对这一新型共识的实现，定义了更宽松的条件，这些条件涉及连接社区内代理与外部代理的边数 $k$，以及每个社区中恶意代理的数量。