  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 where, although global consensus is not reached, some
subsets of agents $V_i$ will still converge to the same values $M_i$ among
themselves. To reach this new type of consensus, we define more relaxed
requirements in terms of the number of malicious agents in each community, and
the number $k$ of edges connecting an agent in a community to agents external
to the community.
