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We consider a community detection problem for gossip dynamics with stubborn agents in this paper. It is assumed that the communication probability matrix for agent pairs has a block structure. More specifically, we assume that the network can be divided into two communities, and the communication probability of two agents depends on whether they are in the same community. Stability of the model is investigated, and expectation of stationary distribution is characterized, indicating under the block assumption, the stationary behaviors of agents in the same community are similar. It is also shown that agents in different communities display distinct behaviors if and only if state averages of stubborn agents in different communities are not identical. A community detection algorithm is then proposed to recover community structure and to estimate communication probability parameters. It is verified that the community detection part converges in finite time, and the parameter estimation part converges almost surely. Simulations are given to illustrate algorithm performance.
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We consider a community detection problem in a gossip model, where agents randomly interact pairwise, with stubborn agents never changing their states. It is assumed that the agents can be divided into two communities based on their interaction probability with others. Such a model can illustrate how disagreement and opinion fluctuation arise in a social network. The considered problem is twofold: to infer which community each agent belongs to, and to estimate interaction probabilities between agents, by only observing their state evolution. First, stability and limit theorems of the model are derived. An integrated detection and estimation algorithm is then proposed to infer the two communities and to estimate the interaction probabilities, based on agent states. It is verified that the community detector of the algorithm converges in finite time, and the interaction estimator converges almost surely. In addition, non-asymptotic property is obtained for the former, and convergence rate is analyzed for the latter. Simulations are presented to illustrate the performance of the proposed algorithm.
We consider optimizing the placement of stubborn agents in a social network in order to maximally influence the population. We assume individuals in a directed social network each have a latent opinion that evolves over time in response to social media posts by their neighbors. The individuals randomly communicate noi
We give a simple distributed algorithm for computing adjacency matrix eigenvectors for the communication graph in an asynchronous gossip model. We show how to use this algorithm to give state-of-the-art asynchronous community detection algorithms when the communication graph is drawn from the well-studied stochastic block model. Our methods also apply to a natural alternative model of randomized communication, where nodes within a community communicate more frequently than nodes in different communities. Our analysis simplifies and generalizes prior work by forging a connection between asynchronous eigenvector computation and Ojas algorithm for streaming principal component analysis. We hope that our work serves as a starting point for building further connections between the analysis of stochastic iterative methods, like Ojas algorithm, and work on asynchronous and gossip-type algorithms for distributed computation.
We consider a network consisting of a single source and $n$ receiver nodes that are grouped into $m$ equal size communities, i.e., clusters, where each cluster includes $k$ nodes and is served by a dedicated cluster head. The source node kee
This paper studies scale-free protocol design for H2 almost state synchronization of homogeneous networks of non-introspective agents in presence of external disturbances. The necessary and sufficient conditions are provided by designing collaborative linear dynamic protocols. The design is based on localized information exchange over the same communication network, which does not need any knowledge of the directed network topology and the spectrum of the associated Laplacian matrix. Moreover, the proposed protocol is scalable and achieves H2 almost synchronization with a given arbitrary degree of accuracy for any arbitrary number of agents.
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