Complex Networks IV pp 155-163
Application of Semidefinite Programming to Maximize the Spectral Gap Produced by Node Removal
- Cite this paper as:
- Masuda N., Fujie T., Murota K. (2013) Application of Semidefinite Programming to Maximize the Spectral Gap Produced by Node Removal. In: Ghoshal G., Poncela-Casasnovas J., Tolksdorf R. (eds) Complex Networks IV. Studies in Computational Intelligence, vol 476. Springer, Berlin, Heidelberg
The smallest positive eigenvalue of the Laplacian of a network is called the spectral gap and characterizes various dynamics on networks. We propose mathematical programming methods to maximize the spectral gap of a given network by removing a fixed number of nodes. We formulate relaxed versions of the original problem using semidefinite programming and apply them to example networks.
Keywordscombinatorial optimization network synchronization random walk opinion formation Laplacian eigenvalue
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