An important concept in complex networks is the degree distribution has a power-law tail. In order to determine the degree exponent of geometric growth networks, people need to use complementary degree distribution. Then, a theoretical problem is proposed: for discrete distributions, if complementary distribution has a power-law tail, distribution has a power-law tail, and vice versa. We found that this conclusion is not true in general. A necessary and sufficient condition that distribution and complementary distribution also has a power-law tail is given in this paper.

By mapping the adjacency matrix of a complex network to Hamiltonian of a quantum system, the statistical properties of the spectra and eigenstates are analyzed. The spectral statistics, i.e. the nearest-neighbor spacing distribution, the number variance and the spectral form factor, are analyzed numerically. The results show that when the rewiring probability of small-world network model is lower, the spectral properties are consistent with those of quantum integrable systems. When the rewiring probability is higher than a certain threshold, its energy spectrum properties are similar to those of the Gaussian orthogonal ensembles in random matrix theory. These results hint that certain analogies may exist between the spatial topology of complex networks and the temporal evolution properties of quantum dynamical systems.

This paper researches scientist TD Lee and his cooperation network. It is found that not only has the common topological properties both of scale-free and small-world for a general scientist cooperation networks, but also appears the creation multiple-peaks phenomenon for number of published paper with year evolution, as well as demonstrates this phenomenon from other scientists, which become a TD Lee significant mark distinguished from other scientists each other. To demonstrate and explain this new finding, we propose a theoretical model for a nature scientist and his/her team innovation ability, which mainly includes two parts of the contribution, one is the first author contribution in his/her papers and the second is the first author contribution in the other cooperation papers, as well as consider their science citations and influence factor of the journal published papers in the cooperation network formed by all his published papers. The theoretical results are consistent with the empirical studies very well. This research demonstrates that the theoretical model has a certain universality and can be extended to estimate innovation ability for any nature scientist and his/her team.

The halo-chaos beam transport network with small world （WS) and scale-free （BA) characteristics was constructed. Several synchronization control methods to realize the synchronization control of halo-chaos and three kinds of circuit schemes for secure communication were proposed and simulation tests were done. Based on the research of chaos complexity, we explore a new method of chaotic algorithm, and successfully develope a data cryptograph prototype, which was applied to telephone communication networks with computer on line experimentally. We also proposed a chaotic encryption system based on combination of chaotic encryption algorithm with traditional algorithm, achieved the hardware developed by FPGA Technology, and realized file encryption and decryption communication experiment on the internet. In the research on information hiding technique, the encryption information is hided in JPEG format images, and the hiding effect is good by testing and engineering application.

Link predictability in complex networks refers to the upper limit for link prediction accuracy by using prediction algorithm, and the analysis of link predictability is conductive to compare the pros and cons for various prediction methods in theory. In this paper, we analyzed the topological distance distribution between two nodes forming a link during the process of multiple networks evolution, and then illustrated the mechanism for making effective link prediction based on common neighbor similarity index. At last, we analyzed the prediction upper limit （predictability) for nine algorithms based on common neighbor similarity in theory. By analyzing the limitation of first order neighbor prediction algorithm and the factor affecting link predictability, we proposed two types of link prediction algorithms based on high order path information and calculated their predictability index. This study proposed the link predictability index in theory, and proved the validity of the proposed link prediction algorithm by predicting real networks.

Currently, the opportunity of integrating research paradigms of complex networks and data mining has come. On the basis of analyzing and comparing these two paradigms, it is pointed out that data mining research community should pay more attention to discovering universal laws and internal mechanisms of the system. For the research of complex networks, data mining techniques should be introduced to handle big data, and an integrated paradigm for the synergistic collaboration between theoretical model construction and data analytics should be formed. Then, exploratory work of the integration of complex networks and data mining has been discussed, and the possible directions for paradigm integration also have been proposed.

By analyzing the mismatching between current Internet architecture and Internet’s mainstream application paradigm, a complementary binary future Internet architecture is proposed in this paper, which consists of a primary structure （the current Internet architecture) and a secondary structure （the broadcast-storage network). This new Internet architecture can not only maintain some irreplaceable advantages and features of the existing Internet architecture, but also bring unprecedented physical revolution for the future Internet.

In this paper, we discuss some application challenges of network science in counter-terrorism research under the big data times. The research focuses on some issues, such as data resource of counter-terrorism network, network evolution and dynamic behavior of terrorism organization network, network control and forecast of counter-terrorism information. These researches provide some directions in future counter-terrorism of network science, which make some progresses in counter-terrorism war.

Complex network is the skeleton of the complex system. It composes of nodes and edges. Most of the networks have some important properties such as the power law degree distribution and the small world effect. Usually, it is not easy to justify the scale free degree distribution and estimate the parameters of the scale free distribution and to quantify both global and local network structure at the same time. In this paper, we will review the main statistics inference methods of complex networks, such as the estimation of parameters in power law distribution and exponential random graph model. Moreover, we also comment these methods from a statistical mathematical standpoint.

The effects of three typical structural properties on invulnerability of complex network topologies are investigated based on the natural connectivity. The effect of degree distribution on invulnerability of complex network topologies is studied by generating complex networks with various degree distributions using mixing preferential attachment model. It is shown that, with the same condition, the more heterogeneous the degree distribution is, the better the invulnerability is. The effect of small-world property on invulnerability of complex network topologies is studied by degree-preserve rewirings and freedom rewirings from regular ring lattices, respectively. It is shown that there is no certain correlation between small-world property and invulnerability. The effect of degree correlation on invulnerability of complex network topologies is studied by degree-preserve-assortativerewirings and degree-preserve-disassortativerewirings, respectively. It is shown that assortative networks are more invulnerable than disassortative networks.

The conventional research method of obesity is generally on the basis of linear models, and only some important factors like genetic, dietary and physical activity have been discussed. Actually, the above linear method is difficult not only for making a comprehensive systematic description and analysis for obesity influence factors, but also for effectively preventing and controlling the adult obesity. In this study, we used the 109 variables in eight categories proposed by the British authority scientists to study obesity, and we qualitatively and quantitatively analyzed the interaction between all the variables and their network topological structure based on complex network theory. Furthermore, we explored important factors of influencing adult overweight and obesity, and we studied the multi-scale correlation among various factors.