Investigations To The Cooperation-competition Networks And Interconnecting Networks

In complex system studies, scientists regard complex systems as the collection of nodes and edges, and then investigate the system properties, structure and evolution by employing graph theory and some other theories and methods. Some achievements are obtained. In recent years, complex network has been widely used in understanding a number of complex systems in social, life science, and technology areas. Complex network is considered as a powerful tool for understanding the complex system and attracts much attention from the scientists in wide fields, such as computer science, biology, mathematics and physics. It becomes an important interdiscipline research project. This thesis reports two major studies on the complex networks:1) empirical and theoretical investigations on the cooperation-competition networks;2) empirical and theoretical investigations on the interconnecting networks. We attempt to get some insights into the underlying physical principle of the complex systems, namely, extracting the common features of the very different real world complex systems and their physical mechanism.Human society is one of the most complex systems; therefore study on the social network attracts attentions. A trend in the studies is to pick-up and to understand the common properties, rules and mechanisms of a type of social systems. The study on so-called "cooperation-competition" systems is an important direction of the studies. At the beginning of the complex network studies, so-called "cooperation network" such as movie actor cooperation networks and scientific coauthorship networks, were considered important. Usually the cooperation systems are described by "affiliation bipartite graphs" in which the basic elements of system are divided to two kinds (äº'补的), i.e., act nodes and actor nodes. Only the edges between different kinds of nodes are considered. One may discuss the projections of the graph onto one kind of nodes. However, scientists gradually realize that, in real world social systems and many large technological or natural systems influenced by human being, the complete cooperation or competition between the elements are the extreme cases and very rare in practice. The systems with simultaneous cooperation and competition between the elements are more common, which are suitable for a cooperation-competition network description. Although many scientists realized the importance of considering the cooperation and competition simultaneously, most of the studies are restricted in qualitative discussion and description, or only for a specific kind of systems. Quantitative investigations on general cooperation-competition systems are still very rare. We conducted a rather systematic study on cooperation-competition networks. The main achivements are:1. As the empirical investigations of the real world networks are the basis for understanding the complex systems, we conducted detailed empirical investigations for19typical cooperation-competition networks. To characterize the cooperation-competition between the elements of the system, our group proposed a quantity, i.e., node weight, to describe the cooperation sharing (or competition gain). The author of this thesis, as one of the major contributors, participated in all the empirical investigations to these cooperation-competition networks.2. The GENI coefficient, which was widely used in economic field, was introduced to describe the distribution heterogeneity of node weight. Particularly, we analytically derived the relationship between the GENI coefficient and the SPL parameters of the node weight distributions, and compared with the empirical results. The analytical results are in good agreement with the empirical observations.3. To understand the general properties of the evolution dynamics of the cooperation-competition networks, we collected the data of the network evolution durations for some of the empirical systems. A strong correlation betweent the evolution durations of the networks and the SPL parameters charactering the node weight distributions was observed. The cooperation-competition systems with longer evolution durations tend to have more heterogeneous distributions of the node weight. Such an empirical observation strongly suggests that the evolution durations of the cooperation-competition networks play dominant role on the distribution of the node weight. Based on such empirical observation, we proposed a general evolution model of the cooperation-competition networks, namely, the evolution of the node weights of the systems are mainly controlled by the Matthew effect dominated evolution dynamics. Consequently, the final distributions of the node weight are mainly determined by the evolution durations of the systems. From this evolution model, we analytically derived the quantitative relationship between the evolution durations and the SPL paramerters and that between the SPL parametrers. The analytical results can well reproduce the empirical observations covering the fields of society, economic, science, traffic, food, and language etc., suggesting that our model captures the essence of the evolution dynamics of the cooperation-competition networks..4. We proposed the concept of competition entropy to describe the competition intensity, and developed an evolution model of the competition entropy. The analytic results based on the evolution model suggest that the systems with longer evolution durations have smaller exponent y (one of the SPL parameters charactering the node weight distributions), which is consistent with the results based on the Matthew effect dominated evolution dynamics of the cooperation-competition networks.The typical complex systems, e.g., biological system and social system, are highly complicated. Most of these systems show layered features, and the sub-systems may show delicate orgonizations. The interactions between the elements of the same system can be very different, and the elements and/or sub-systems are strongly interdependent to each other. All these features make the characterization of the complex systems extremely difficult. Consequently, in understanding these complex systems, people usually make drastic simplifications and assume that the systems comprise one kind of elements with the same interaction feature. Therefore, most of the previously discussed networks were limited to the isolated networks, which contain only one kind of nodes and interactions, without considering the correlation between different networks. However, these networks are often a part of larger complex systems, and their topological properties are often correlated and dependent to each other, which suggests that a typical complex system should be described by a supernetwork (we can also call it network of networks or interdependent network) in which the conventional networks are related by a higher level network. In recent years, such more systematic descriptions to complex networks are becoming an attracting research area. For example, in august of2010, the committee of Chinese complex system and complex network asscociation decided to set the research of "network of networks" as the most important target of the future studies following the suggestions of the supervisor of the author of this thesis. Due to the difficulty of such studies, some people choose to start with some interdependent networks comprising small number of subnetworks, which were usually called as multilayer network). In this thesis, we conducted some empirical and theoretical investigations to the multilayer networks. The main achivements are: 1. We introduced a new kind of interdependent multilayer networks, i.e., interconnecting networks, in which the component networks are coupled to each other by sharing some common nodes. The common nodes shared by the component networks are referred to as interconnecting nodes. Such interconnecting networks represent the cases in which the elements play different roles in different networks. It is common to observe such interconnection of network layers in real world complex systems. This kind of interconnecting networks may be the most straightforward manner to realize the coupling between the networks. Revealing the features of the interconnecting networks is important for understanding the general properties of the multilayer networks.2. We proposed a very simple model of the evolution of the interconnecting networks, and analytically derived a quantitative function describing the common feature of such bilayer interconnecting networks (i.e., the networks with larger averaged topological differences of the interconnecting nodes tend to share fewer nodes). The analytic results are in good agreement with the empirical observsations of8bilayer interconnecting networks covering the fields of biology, science activity, traffic, food, and medicine. The node sharing mechanism (which is the basis of the model assumption), namely, the difference of the topological properties of the interconnecting nodes is proportional to the average of the topological properties of each node in the two layers, is also supported by the empirical data. Based on this node sharing rule, the empirically observed correlation between the averaged topological differences and the interconnecting node number can be well reproduced.