Abstract:In order to improve network controllability, a network controllability improvement method based on graph convolutional neural network is proposed, in which a graph convolutional network is first trained to select appropriate nodes, and then edges are randomly added between these selected nodes. Numerical simulations are carried out on two representative complex network models. Compared with the traditional method in which edges are added randomly between all nodes, the proposed method greatly reduces the number of added edges, which is more efficient.
[1] BARABÁSI A L. Network science[J]. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2013, 371(1987): 20120375. [2] STROGATZ S H. Exploring complex networks[J]. Nature, 2001, 410(6825): 268276. [3] PAGANI G A, AIELLO M. The power grid as a complex network: a survey[J]. Physica A: Statistical Mechanics and Its Applications, 2013, 392(11): 26882700. [4] HÁZNAGY A, FI I, LONDON A, et al. Complex network analysis of public transportation networks: a comprehensive study[C]//2015 International Conference on Models and Technologies for Intelligent Transportation Systems (MT-ITS), Budapest:IEEE, 2015: 371378. [5] KISS I Z, BERTHOUZE L, TAYLOR T J, et al. Modelling approaches for simple dynamic networks and applications to disease transmission models[J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2012, 468(2141):1332-1355. [6] GOSAK M, MARKOVIČ R, DOLENEK J, et al. Network science of biological systems at different scales: A review[J]. Physics of Life Reviews, 2018, 24: 118135. [7] SKVORETZ J. Complexity theory and models for social networks[J]. Complexity, 2002, 8(1): 4755. [8] CSARDI G, NEPUSZ T. The igraph software package for complex network research[J]. Complex Systems, 2006, 1695(5): 19. [9] BOCCALETTI S, LATORA V, MORENO Y, et al. Complex networks: Structure and dynamics[J]. Physics Reports, 2006, 424(4/5): 175308. [10] LIU Y Y, SLOTINE J J, BARABÁSI A L. Controllability of complex networks[J]. Nature, 2011, 473(7346): 167173. [11] GALIL Z. Efficient algorithms for finding maximum matching in graphs[J]. ACM Computing Surveys (CSUR), 1986, 18(1): 2338. [12] YUAN Z, ZHAO C, DI Z, et al. Exact controllability of complex networks[J]. Nature Communications, 2013, 4(1): 2447. [13] GAO J, LIU Y Y, D′SOUZA R M, et al. Target control of complex networks[J]. Nature Communications, 2014, 5(1): 5415. [14] LOU Y, WANG L, CHEN G. A framework of hierarchical attacks to network controllability[J]. Communications in Nonlinear Science and Numerical Simulation, 2021, 98: 105780. [15] CHEN G. Controllability robustness of complex networks[J]. Journal of Automation and Intelligence, 2022, 1(1): 27. [16] LECUN Y, BENGIO Y, HINTON G. Deep learning[J]. Nature, 2015, 521(7553): 436444. [17] DONG S, WANG P, ABBAS K. A survey on deep learning and its applications[J]. Computer Science Review, 2021, 40: 100379. [18] KIPF T N, WELLING M. Semi-supervised classification with graph convolutional networks[DB/OL].[20230915].https://arxiv.org/pdf/1609.02907. [19] ZHANG S, TONG H, XU J, et al. Graph convolutional networks: a comprehensive review[J]. Computational Social Networks, 2019, 6(1): 123. [20] BOTH C, DEHMAMY N, YU R, et al. Accelerating network layouts using graph neural networks[J]. Nature Communications, 2023, 14(1): 1560. [21] MOTTER A E, LAI Y C. Cascade-based attacks on complex networks[J]. Physical Review E, 2002, 66(6): 065102. [22] HOQUE N, BHUYAN M H, BAISHYA R C, et al. Network attacks: Taxonomy, tools and systems[J]. Journal of Network and Computer Applications, 2014, 40: 307324. [23] WU Y, WEI D, FENG J. Network attacks detection methods based on deep learning techniques: a survey[J]. Security and Communication Networks, 2020, 1: 117. [24] YAN X Y, WANG W X, CHEN G R, et al. Multiplex congruence network of natural numbers[J]. Scientific Reports, 2016, 6(1): 23714. [25] BLATTER J, HAVERLAND M. Congruence Analysis[M]. London: Palgrave Macmillan UK, 2012: 144204. [26] LOU Y, WANG L, CHEN G. Toward stronger robustness of network controllability: a snapback network model[J]. IEEE Transactions on Circuits and Systems I: Regular Papers, 2018, 65(9): 29832991. [27] ALBERT R, BARABÁSI A L. Statistical mechanics of complex networks[J]. Reviews of Modern Physics, 2002, 74(1): 47. [28] ERDÖS P, RÉNYI A. On the evolution of random graphs[J]. Publ Math Inst Hung Acad Sci, 1960, 5(1): 1760. [29] BARABÁSI A L, ALBERT R. Emergence of scaling in random networks[J]. Science, 1999, 286(5439): 509512. [30] BRANDES U. A faster algorithm for betweenness centrality[J]. Journal of Mathematical Sociology, 2001, 25(2): 163177.