| KEYWORD |
Optimization and robustness of network centrality
keywords COMPLEX SYSTEMS, NETWORK DYNAMICS, NETWORKS THEORY, OPTIMIZATION
Reference persons GIACOMO COMO, FABIO FAGNANI
Research Groups Analisi e controllo di sistemi dinamici
Description Notions of networks centrality such as eigenvector, Katz, Bonacich, and PageRank centralities allow to measure the relative influence of the different nodes in a network. A very relevant issue concerns the dependance of these centrality measures on relatively small changes in the network (i.e., changes that directly affect one or a small fraction of nodes). In this thesis, some network centrality optimization problems (e.g., what is the optimal way to add a out-link from a node i in order to increase the centrality of another node j) will be studied using techniques from stochastic matrix theory and the electrical network analogies. Moreover, fundamental robustness bounds relating changes in the network to changes in the node centralities will be derived.
[1] G. Como and F. Fagnani, “Robustness of large-scale stochastic matrices to localized perturbations,” IEEE Transactions on Network Science and Engineering, 2 (2), pp. 1-12, 2015.
[2] F. Fagnani and J.C. Delvenne, “The robustness of democratic consensus,” Automatica, 52, pp. 232-241, 2015.
[3] L. Vassio, F. Fagnani, P. Frasca, and A. Ozdaglar, “Message-passing optimization of network centrality”, IEEE Transactions on Control of Network Systems, 1, pp. 109-120, 2014.
[4] R. Hollanders, G. Como, R. Jungers, and J.-C. Delvenne, “Tight bounds on sparse perturbations of Markov chains“, 2015.
Deadline 17/07/2019
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