[1]LIU Shengjiu,LI Tianrui,HORNG Xijin,et al.Supernetwork building based on matrix operation and property analysis[J].CAAI Transactions on Intelligent Systems,2018,13(3):359-365.[doi:10.11992/tis.201706055]
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Supernetwork building based on matrix operation and property analysis

CAAI Transactions on Intelligent Systems[ISSN 1673-4785/CN 23-1538/TP] Volume: 13 Number of periods: 2018 3 Page number: 359-365 Column: 学术论文—智能系统 Public date: 2018-05-05
Title:
Supernetwork building based on matrix operation and property analysis
Author(s):
LIU Shengjiu1; 2;  LI Tianrui1; 2;  HORNG Xijin1; 2; 3;  WANG Hongjun1; 2;  ZHU Jie1; 2; 4
1. School of Information Science and Technology, Southwest Jiaotong University, Chengdu 611756, China;
2. Sichuan Key Lab of Cloud Computing and Intelligent Technique, Southwest Jiaotong University, Chengdu 611756, China;
3. Department of Computer Science and Information Engineering, National Taiwan University of Science and Technology, Taipei 10607, China;
4. Department of Computer Science, Tibetan University, Lhasa 850000, China
Keywords:
matrix operation; complex network; supernetwork; model building; fractal dimension; self-similarity supernetwork; random supernetwork; property analysis
CLC:
TP393
DOI:
10.11992/tis.201706055
Abstract:
We study supernetwork building based on the Khatri-Rao product operation and the Khatri-Rao sum operation on adjacency matrices. In addition, the marginal-and joint-node degrees are introduced to investigate the mechanism of a supernetwork. The Khatri-Rao product operation is iteratively applied to a simple initial network to form the adjacent supernetwork matrix and obtain a self-similarity supernetwork with fractal dimensions of no longer than 3. If all initial networks are connected with nonbipartite graphs, the obtained supernetwork has a diameter that does not exceed twice the summation of all initial networks. Furthermore, the Khatri-Rao sum operation is sequentially applied to multiple simple initial networks to form adjacency matrices of supernetwork and obtain a random supernetwork with one marginal node degree, with one-dimensional Gaussian distribution, and a joint node degree, with a high-dimensional Gaussian distribution. Finally, several properties of the proposed supernetwork building based on matrix operation are presented.
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