【作者】 李季明； 张宁；

【Author】 Jiming Li, Ning Zhang (Business School and Institute of Systems Engineering , University of Shanghai for Science and Technology, Shanghai 200093, China)

【机构】 上海理工大学管理学院系统工程研究所；

【摘要】 现实生活中存在着各种各样的复杂网络,研究者们在以往的复杂网络研究过程中提出了多种研究模型,但是大多的网络模型都是随机模型,不易于直观理解网络的特性;为了更好的理解某些复杂网络的特性,本文借鉴文献[8]的建模思想,给出了一种通过边的迭代生成确定性网络模型的算法。通过分析算法和模型的演化图形,对网络模型的平均度、度分布和群聚系数做了推导,得出此确定性网络模型的平均度和群聚系数在迭代步数趋于无穷大时趋于一个确定的值, 而度分布为一个确定性的离散指数分布。更多还原

【Abstract】 Complex networks are ubiquitous in real-life world, researchers have given many kinds of complex network models in former researches, but most models are stochastic, the randomness makes it more difficult to understand the complex networks characteristics. For better understanding the characteristics of complex networks, this text presents a model that generates a network model by edge iterations on the base of reference [8]. By analyzing the model’s algorithm and evolution graph, deduce the network model’s average degree, degree distribution and clustering coefficient. As a result, the deterministic network’s average degree and clustering coefficient tend to a constant, when the iterative step tends to infinite and has a discrete exponential degree distribution. Based on the regular network, W-S small-world network, random network and algorithms generated by deterministic network models, we simulated networks average degree, clustering coefficient, average path length and degree distribution with MATLAB programs on the computer. Through analyzing the simulated data and theory deduce, we know that the deterministic network also has small-world networks characteristic -large clustering coefficient and small average path length -and has completely random networks characteristic -exponential degree distribution.更多还原