Research On The Impact Of Topology Growing Network Evolution

The structure is always inevitably one of the most basic issues in the study of complex networks among a large variety of research areas, whether from neurobiology to statistical physics, or from engineering to economics and sociology. Topology is the foundation of either constructing models for complex systems or investigating the characteristics, functions and behaviour of complex systems. Studies on how or to what extent the topology will impose an influence on network evolution will no doubt not only contribute to a better understanding of a variety of categories of complex networks existing in the real world, but also will it definitely bring important inspiration to the optimization and design of artificial complex engineering systems.In this paper, we focused on the impact of topology during the evolution of complex networks, under the influence of both network growth and target function. We drive networks of distinct topologies evolving toward predetermined target function on the classical Boolean Network model by applying several different kinds of growing rules on the network evolution. We employed genetic algorithms to perform extensive simulations, and examined in detail the evolutionary performance of networks with different types of topologies. The results demonstrated that: (1) When evolving to the pre-established target function with a concurrent dynamic network growth, the scale-free network displays a slightly better performance than its random counterpart in two ways: one is that in the early stage of network evolution the scale-free network can converge to the target function more quickly, and the other is that the scale-free network is also able to escape more fast when caught in local extremum. But meanwhile, due to the influence of node growth, both scale-free and random network have shown obvious degradation on their performance after the mid-term of the evolution and finally deteriorate to almost the same very weak evolutionary capability. (2) The evolutionary performance tend to be raised when the average connectivity increased both for scale-free network and random network, but there is an obvious bottleneck for far more promotion.(3) During the network growth, the interval that a new node is added has obvious effects on the evolutionary performance, that is, the more frequently the node increases, the relatively faster the network evolves. (4) When scale-free network compete with random network in the same population, they do not show evolutionary advantage over each other. (5) Scale-free network with disassortative mixing feature exhibits a more faster and more robust evolutionary performance than the assortative mixing one.In short, this paper reveals the impact of the topological structure on the dynamic growing complex network when evolving to pre-defined target function. It benefits us to develop a more comprehensive understanding of the relationship among structure, function and evolution of the complex networks .