1. Distributed estimation and control of node centrality in undirected asymmetric networks
- Author
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Andrea Gasparri, Gabriele Oliva, Eduardo Montijano, Montijano, Eduardo, Oliva, Gabriele, and Gasparri, Andrea
- Subjects
0209 industrial biotechnology ,Theoretical computer science ,Social network ,Computer science ,Generalization ,business.industry ,Node (networking) ,Control (management) ,Eigenvector centrality ,02 engineering and technology ,Systems and Control (eess.SY) ,16. Peace & justice ,Electrical Engineering and Systems Science - Systems and Control ,Graph ,Computer Science Applications ,020901 industrial engineering & automation ,Control and Systems Engineering ,Distributed algorithm ,Convergence (routing) ,FOS: Electrical engineering, electronic engineering, information engineering ,Electrical and Electronic Engineering ,Focus (optics) ,business ,Centrality ,Protocol (object-oriented programming) - Abstract
Measures of node centrality that describe the importance of a node within a network are crucial for understanding the behavior of social networks and graphs. In this paper, we address the problems of distributed estimation and control of node centrality in undirected graphs with asymmetric weight values. In particular, we focus our attention on $\alpha$-centrality, which can be seen as a generalization of eigenvector centrality. In this setting, we first consider a distributed protocol where agents compute their $\alpha$-centrality, focusing on the convergence properties of the method; then, we combine the estimation method with a consensus algorithm to achieve a consensus value weighted by the influence of each node in the network. Finally, we formulate an $\alpha$-centrality control problem which is naturally decoupled and, thus, suitable for a distributed setting and we apply this formulation to protect the most valuable nodes in a network against a targeted attack, by making every node in the network equally important in terms of {\alpha}-centrality. Simulations results are provided to corroborate the theoretical findings., Comment: published on IEEE Transactions on Automatic Control https://ieeexplore.ieee.org/abstract/document/9126182
- Published
- 2019
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