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We consider a community detection problem for gossip dynamics with stubbornagents in this paper. It is assumed that the communication probability matrixfor agent pairs has a block structure. More specifically, we assume that thenetwork can be divided into two communities, and the communication probabilityof two agents depends on whether they are in the same community. Stability ofthe model is investigated, and expectation of stationary distribution ischaracterized, indicating under the block assumption, the stationary behaviorsof agents in the same community are similar. It is also shown that agents indifferent communities display distinct behaviors if and only if state averagesof stubborn agents in different communities are not identical. A communitydetection algorithm is then proposed to recover community structure and toestimate communication probability parameters. It is verified that thecommunity detection part converges in finite time, and the parameter estimationpart converges almost surely. Simulations are given to illustrate algorithmperformance.

Community Detection for Gossip Dynamics with Stubborn Agents