A nonlinear spectral method for core-periphery detection in networks

Abstract

We derive and analyse a new iterative algorithm for detecting network core–periphery structure. Using techniques in nonlinear Perron-Frobenius theory, we prove global convergence to the unique solution of a relaxed version of a natural discrete optimization problem. On sparse networks, the cost of each iteration scales linearly with the number of nodes, making the algorithm feasible for large-scale problems. We give an alternative interpretation of the algorithm from the perspective of maximum likelihood reordering of a new logistic core–periphery
random graph model. This viewpoint also gives a new basis for quantitatively judging a core–periphery detection algorithm. We illustrate the algorithm on a range of synthetic and real networks, and show that it offers advantages over the current state-of-the-art.

Please cite this paper as:

@article{tudisco2018core,
  title = {A nonlinear spectral method for core-periphery detection in networks},
  author = {Tudisco, Francesco and Higham, Desmond J.},
  journal = {SIAM J. Mathematics of Data Science},
  volume = {1},
  pages = {269-292},
  year = {2019}
}

Keywords: Core-periphery meso-scale structure networks Perron-Frobenius theory nonlinear eigenvalues spectral method spectral clustering nonnegative matrices power method