A Nonlinear Spectral Method for Core-Periphery Detection in Networks

Francesco Tudisco, Desmond J. Higham

Abstract: We derive and analyze a new iterative algorithm for detecting network core--periphery structure. Using techniques from 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 presents 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.