A nonlinear spectral method for core-periphery detection in networks

Francesco Tudisco, Desmond Higham

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Article number1
Pages (from-to)269-292
Number of pages24
JournalSIAM Journal on the Mathematics of Data Science (SIMODS)
Issue number2
Publication statusPublished - 11 Apr 2019


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