第3期 刘胜久，等：基于矩阵运算的超网络构建方法研究及特性分析 ·365· tures in complex systems and complex networks[J].Com- equations and their applications to characterization of prob- plex systems and complexity science,2006,3(4):41-51. ability distributions[J].Sankhya:the Indian journal of stat- [9]GALICEANU M,REIS A S,DOLGUSHEV M.Dynamics istics,series A,1968,30(2):167-180. of semiflexible scale-free polymer networks[].The journal [17]TRACY D S,SINGH R P.A new matrix product and its of chemical physics,2014,141(14):144902. applications in partitioned matrix differentiation[J].Statist- [10]刘胜久，李天瑞，洪西进，等.基于矩阵运算的复杂网络 ica neerlandica.1972.26(4):143-157. 构建方法).中国科学：信息科学，2016,46(5)：610-626. [18]LIU Shuangzhe.Matrix results on the Khatri-Rao and LIU Shengjiu,LI Tianrui,HORNG Shijinn,et al.Complex tracy-singh products[J].Linear algebra and its applications, network construction based on matrix operation[J].Scien- 1999,2891/2/3):267-277. tia sinica informationis,2016,46(5):610-626 [19]SREENIVASAN K R,MENEVEAU C.The fractal facets [1]徐明明，陆君安，周进.两层星形网络的特征值谱及同步 of turbulence[J].Journal of fluid mechanics,1986,173: 能力[).物理学报，2016,65(2)：028902. 357-386. XU Mingming,LU Jun'an,ZHOU Jin.Synchronizability [20]MASSOPUST P R.Fractal functions,fractal surfaces,and and eigenvalues of two-layer star networks[J].Acta phys- wavelets[M].San Diego:Academic Press,1994:135-355. ica sinica,2016,65(2):028902. 作者简介： [12]刘胜久，李天瑞，洪西进，等.超网络模型构建及特性分 刘胜久，男，1988年生，博士，主 析).计算机科学与探索，2017,11(2)：194-211 要研究方向为复杂网络、自然语言处 LIU Shengjiu,LI Tianrui,HORNG Shijinn,et al.Hyper- 理、云计算。发表学术论文10余篇。 network model and its properties[J].Journal of frontiers of computer science and technology,2017,11(2):194-211. [13]BARBE A M.On a class of fractal matrices (I)Excess- Matrices and their self-similar properties[J].International journal of bifurcation and chaos,1992.2(4):841-860. 李天瑞，男，1969年生，教授，博 士生导师，主要研究方向为数据挖掘 [14]BARBE A M.Artistic design with fractal matrices[J].The 与知识发现、粒计算与粗糙集、云计算 visual computer,1993,9(5):233-238. 与大数据。发表学术论文240余篇， [15]SHALLIT J,STOLFI J.Two methods for generating 主持科技项目20余项，其中国家级项 fractals[J].Computers&graphics,1989,13(2):185-191. 目6项。 [16]KHATRI C G,RAO C R.Solutions to some functionaltures in complex systems and complex networks[J]. Com￾plex systems and complexity science, 2006, 3(4): 41–51. GALICEANU M, REIS A S, DOLGUSHEV M. Dynamics of semiflexible scale-free polymer networks[J]. The journal of chemical physics, 2014, 141(14): 144902. [9] 刘胜久, 李天瑞, 洪西进, 等. 基于矩阵运算的复杂网络 构建方法[J]. 中国科学: 信息科学, 2016, 46(5): 610–626. LIU Shengjiu, LI Tianrui, HORNG Shijinn, et al. Complex network construction based on matrix operation[J]. Scien￾tia sinica informationis, 2016, 46(5): 610–626. [10] 徐明明, 陆君安, 周进. 两层星形网络的特征值谱及同步 能力[J]. 物理学报, 2016, 65(2): 028902. XU Mingming, LU Jun’an, ZHOU Jin. Synchronizability and eigenvalues of two-layer star networks[J]. Acta phys￾ica sinica, 2016, 65(2): 028902. [11] 刘胜久, 李天瑞, 洪西进, 等. 超网络模型构建及特性分 析[J]. 计算机科学与探索, 2017, 11(2): 194–211. LIU Shengjiu, LI Tianrui, HORNG Shijinn, et al. Hyper￾network model and its properties[J]. Journal of frontiers of computer science and technology, 2017, 11(2): 194–211. [12] BARBÉ A M. On a class of fractal matrices (I) Excess￾Matrices and their self-similar properties[J]. International journal of bifurcation and chaos, 1992, 2(4): 841–860. [13] BARBÉ A M. Artistic design with fractal matrices[J]. The visual computer, 1993, 9(5): 233–238. [14] SHALLIT J, STOLFI J. Two methods for generating fractals[J]. Computers & graphics, 1989, 13(2): 185–191. [15] [16] KHATRI C G, RAO C R. Solutions to some functional equations and their applications to characterization of prob￾ability distributions[J]. Sankhyā: the Indian journal of stat￾istics, series A, 1968, 30(2): 167–180. TRACY D S, SINGH R P. A new matrix product and its applications in partitioned matrix differentiation[J]. Statist￾ica neerlandica, 1972, 26(4): 143–157. [17] LIU Shuangzhe. Matrix results on the Khatri-Rao and tracy-singh products[J]. Linear algebra and its applications, 1999, 289(1/2/3): 267–277. [18] SREENIVASAN K R, MENEVEAU C. The fractal facets of turbulence[J]. Journal of fluid mechanics, 1986, 173: 357–386. [19] MASSOPUST P R. Fractal functions, fractal surfaces, and wavelets[M]. San Diego: Academic Press, 1994: 135–355. [20] 作者简介： 刘胜久，男，1988 年生，博士，主 要研究方向为复杂网络、自然语言处 理、云计算。发表学术论文 10 余篇。 李天瑞，男，1969 年生，教授，博 士生导师，主要研究方向为数据挖掘 与知识发现、粒计算与粗糙集、云计算 与大数据。发表学术论文 240 余篇， 主持科技项目 20 余项，其中国家级项 目 6 项。 第 3 期 刘胜久，等：基于矩阵运算的超网络构建方法研究及特性分析 ·365·