合作网络及合作竞争网络的相关研究

【作者】 傅春花；

【导师】 何大韧；

【作者基本信息】 扬州大学 ， 理论物理， 2009， 硕士

【摘要】 在经典力学和经典电磁学中,研究的对象——运动物质,被想象为已经被分割为无限多个无限小,且在空间连续分布的基本单元的集合。这些基本单元被想象地放在规则空间中的各个规则格点位置上,因此使用许多年前数学家们创造的坐标体系就可以完善地描述所有基本单元的位置及其变化,即这个体系的运动。尽管各个基本单元的空间位置不同,而且一般来说在随时间变化,但是由于它们之间的相互作用遵从已经被认识的简单、普适基本法则,因此运用几百年前创立的微积分工具就可以非常简明地表示支配每一大类客观体系运动变化的普遍动力学规律。然而,世界上的客观系统是规则、均匀分布的,全同的基本单元构成的,还是高度不规则、不均匀分布的,丰富多彩的基本单元构成的?基本单元的位置分布影响系统的动力学行为吗?基本单元之间的相互作用是遵从某种简单、普适法则,还是千变万化、错综复杂?这可能是物理学推广向复杂系统时要回答的首要问题。复杂网络应运而生,成为研究复杂系统的强有力工具。网络描述建立在简化描述模型的基础上,是对复杂世界的简化、抽象。这样的描述把基本单元看成是网中的一个“节点”,把基本单元之间的相互作用看作节点之间的“边”。在此基础上,提出了一系列的反映网络结构、特征的网络统计性质,如度分布、项目度分布、集群系数、度中心度、同类性等等。复杂网络,尤其是社会网络的一个显著特征是,网络具有明显的群落、派系结构。本文的第二章主要研究了社会网络及类社会网络中的派系结构,提出了网络的新统计量——k方组项目度及其分布。并给出了简化的网络演化模型和解析,然后实证统计了十多个系统的二方组、三方组项目度及其分布,发现我们所研究的实际系统的二方组项目度分布和三方组项目度分布均为SPL分布,具有一定的普遍性,与模型得到的结论是一致的。系统内部基本单元之间的相互作用是极其复杂多样的,若只考虑节点之间的相互合作关系,而忽略其他所有的相互作用(如竞争等关系),这样的网络称为合作网络,将主要反映网络中节点之间合作关系的统计性质,如项目大小、项目度等,称为网络的合作性质。本文的第四章主要报道了四个实际系统的特殊合作性质,并给度分布与项目度分布的一致性提供了更多的实证。然而,实际情况下,基本单元之间不仅存在合作关系,还存在着竞争关系,基本单元之间既合作又竞争是更为普遍的,像这样的网络称为合作竞争网络。既然合作竞争网络是普遍存在的,那么应该如何去描述基本单元之间的合作竞争关系?为此,我们提出了新的统计量——点权,它反映了合作竞争的结果。而且,通过我们的实证统计,发现实际网络的节点总权分布遵循SPL分布,也具有一定的普遍性。本文的第三章和第五章着重研究了合作竞争网络,及点权这一统计量在合作竞争网络中的统计规律。更多还原

【Abstract】 In classical mechanics and classical electromagnetics, the investigation object, motorial matter, considered as been divided into infinitude parts, which tend to be infinitesimal and are consecutive distributed. Motorial matter is regarded as a collection of such parts. These basic parts supposed to be put on regular grid points in the regular space. Therefore, coordinate system, created by mathematician many years ago, can be used to describe the position and position change of all basic parts perfectly. Although every basic part’s position in the space is different, generally changing with time, their mutual actions obey simple and universal recognized basic principles. So we can use calculous theory, founded hundreds of years ago, to show universal dynamic laws dominated these external systems.However, are external systems regular or irregular, even distributed or uneven distributed? Are they composed of uniform basic cells or abundant disparate basic cells? Does the position distribution of basic cells affect system’s dynamic behavior? This may be the first chief question to be answer when physics extend to complex systems. Complex network emerges as the times require and becomes a powerful tool to investigate complex systems. Netwok description based on simply described models. It’s predigestion and abstract of complex world. Such kind of description regarded basic cells as“nodes”in the network and their mutual actions as“edges”between nodes. Then put forward a series of network properties, such as degree distribution, act degree distribution, clustering coefficient, assortativity and so on.There is a very notable character in complex networks, especially social networks. That is this kind of networks have obvious community and clique structure. We mostly investigated clique structures of social and quasi-social networks in chapter three of this paper. A new statistical network property is proposed here. We called it k-clique act degree distribution. Then proposed a simplified network evolvement model and presented detailed analysis of this model. Finally, we did a lot of empirical statistical work. Two-clique act degree distribution and three-clique act degree distribution of many real networks were presented in chapter two. Amazingly, nearly all the distributions we got followed shifted power law (i.e. SPL) distribution, which accorded with the model conclusion. We confered this conclusion maybe universal in a certain extent.As we know, mutual actions between basic cells in real systems are very complicated and various. If we just consider their collaboration and neglect all the other mutual actions, for example the competion relations, the networks are called collaboration networks in this way. And statistical network properties which mainly show collaboration relations between nodes in the network are called collaboration properties, such as act size, act degree and so forth. We have studied four real systems and their special collaboration properties in chapter four.In fact, there is not only collaboration but also competion between basic cells in real systems. It should be more universal that collaboration and competion coexists. Such networks are called collaboration-competion networks in this paper. Since collaboration-competion networks exists universally, how should we describe this kind of collaboration and competion actions? Therefor, we proposed a new property called node weight, which reflects the competion result. Then we calculated total node weight distributions of more than ten real world networks. Surprisingly, all the gained distributions followed SPL distribution. This may be a universal law too. Chapter three and five mainly investigated collaboration-competion networks and the statistical law of node weight in ollaboration-competion networks.更多还原