Review of the network risk propagation research

Through the gradually understanding to the real world, it is beginning to know that the actual structure of many systems expressed in the form of networks. Such as the Internet, the Gene Network, and the Scientists Collaborative Network. However, before the emergence of Complex Network concept, the homogeneous network proposition was more familiar. There are the same characteristics of all units in net with the corresponding significance of all nodes and edges. For a Random Network, because of the equal probability between any two nodes, the degree distribution is a binomial distribution. When the network tends to infinity, the degree distribution of nodes tends to be Poisson distribution. But, after some practical work finished, people gradually found that the majority of real networks degree distributions have power-law characteristics rather than being distributed around an absolute mean value with a certain second-order average. Following with the published paper in Nature, Watts and his mentor Strogatz1 introduced a small world network model and described the transition from an entirely regular system to a fully Random Network. People realized that the small world network has two features both with the clustering characteristics similar to a regular system and the shorter average path length like Random Network. Later, Barabási & Albert2 addressed an article in Science indicated that the degree distribution of many actual Complex Networks obeys the power-law with the scalefree feature. Those systems can be called the Scale-free Network. Since that time, scientists have studied a large number of topological networks, including social networks,3‒7 information networks,8‒11 professional networks12,13 and biological networks,14,15 and others. The results show that these networks have characteristics such as short feature path, high clustering coefficient, degree correlation and community structures. These discoveries have significantly contributed to the study of Complex Networks. The Complex Network and other related network research methods had become one of the main tools for the study of complex systems. Lots of Complex Network models have emerged and caused people’s attention.16‒19 Due to the indepth understanding of the network structure, there are a variety of dynamic processes in the system and the cross-integration with other disciplines in recent years. Researchers studied the single or group dynamics behavior and processes on the network by considering the Complex Network as a dynamical system or quoting moving units into the network, including Communication, Chaos, Robustness, Fractal, Cascading Failures, and Synchronization. Explored the structural characteristics of the whole system and forecasted the links through the analysis about the critical nodes and paths. Designed new algorithms to optimize the network structure and improved the performance, especially regarding stability, synchronization, and data.