Random node reinforcement and K-core structure of complex networks

Ma，Rui1,2; Hu，Yanqing3; Zhao，Jin Hua1,2,4

2023-08-01

10.1016/j.chaos.2023.113706

Chaos, Solitons and Fractals   Impact Factor & Quartile

0960-0779

1873-2887

To enhance robustness of complex networked systems, a simple method is introducing reinforced nodes which always function during failure propagation. A random scheme of node reinforcement can be considered as a benchmark for finding an optimal reinforcement solution. Yet there still lacks a systematic evaluation on how node reinforcement affects network structure at a mesoscopic level upon failures. Here we study this problem through the lens of K-cores of networks. Based on an analytical percolation framework, we first show that, on uncorrelated random graphs, with a critical size of reinforced nodes, an abrupt emergence of K-cores is smoothed out to a continuous one, and a detailed phase diagram is derived. We then show that, with a cost–benefit analysis on random reinforcement, for proper weight factors in cost functions with constant and increasing marginal costs, a gain function shows a unimodality, thus we can analytically find an optimal reinforcement fraction by locating the maximal gain. In all, our framework offers a gain-oriented analytical perspective to designing robust interconnected systems.

K-core percolation Network robustness Node reinforcement

SCI

English

Others

National Natural Science Foundation of China[12171479];National Natural Science Foundation of China[12275118];Natural Science Foundation of Guangdong Province[2020B1515020052];Basic and Applied Basic Research Foundation of Guangdong Province[2022A1515011765];

Mathematics ; Physics

Mathematics, Interdisciplinary Applications ; Physics, Multidisciplinary ; Physics, Mathematical

WOS:001040629800001

PERGAMON-ELSEVIER SCIENCE LTD

PHYSICS

2-s2.0-85162935335

Scopus

1.Guangdong Provincial Key Laboratory of Nuclear Science,Institute of Quantum Matter,South China Normal University,Guangzhou,510006,China
2.Guangdong-Hong Kong Joint Laboratory of Quantum Matter,Southern Nuclear Science Computing Center,South China Normal University,Guangzhou,510006,China
3.Department of Statistics and Data Science,College of Science,Southern University of Science and Technology,Shenzhen,518055,China
4.School of Data Science and Engineering,South China Normal University,Shanwei,516622,China

Ma，Rui,Hu，Yanqing,Zhao，Jin Hua. Random node reinforcement and K-core structure of complex networks[J]. Chaos, Solitons and Fractals,2023,173.

Ma，Rui,Hu，Yanqing,&Zhao，Jin Hua.(2023).Random node reinforcement and K-core structure of complex networks.Chaos, Solitons and Fractals,173.

Ma，Rui,et al."Random node reinforcement and K-core structure of complex networks".Chaos, Solitons and Fractals 173(2023).