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A Fast and Exact Greedy Algorithm for the Core–Periphery Problem

Department of Mathematics, Computer Science and Physics, University of Udine, 33100 Udine, Italy
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Symmetry 2020, 12(1), 94; https://doi.org/10.3390/sym12010094
Received: 6 December 2019 / Revised: 27 December 2019 / Accepted: 30 December 2019 / Published: 3 January 2020
(This article belongs to the Special Issue Symmetry in Numerical Linear and Multilinear Algebra)
The core–periphery structure is one of the key concepts in the structural analysis of complex networks. It consists of a partitioning of the node set of a given graph or network into two groups, called core and periphery, where the core nodes induce a well-connected subgraph and share connections with peripheral nodes, while the peripheral nodes are loosely connected to the core nodes and other peripheral nodes. We propose a polynomial-time algorithm to detect core–periphery structures in networks having a symmetric adjacency matrix. The core set is defined as the solution of a combinatorial optimization problem, which has a pleasant symmetry with respect to graph complementation. We provide a complete description of the optimal solutions to that problem and an exact and efficient algorithm to compute them. The proposed approach is extended to networks with loops and oriented edges. Numerical simulations are carried out on both synthetic and real-world networks to demonstrate the effectiveness and practicability of the proposed algorithm. View Full-Text
Keywords: complex networks; core–periphery structure; combinatorial optimization; greedy algorithm; power-law networks complex networks; core–periphery structure; combinatorial optimization; greedy algorithm; power-law networks
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Fasino, D.; Rinaldi, F. A Fast and Exact Greedy Algorithm for the Core–Periphery Problem. Symmetry 2020, 12, 94.

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