Испитивање својстава комплексних мрежа са дискретном динамиком

Abstract

Комплексне мреже су се у току последње две деценије показале као изузетно користан концепт у проучавању карактеристика комплексних система...

In the last two decades, complex networks have been proven as very useful concept for examination of properties of complex systems. The first step within this framework is to extract individual elements of the system and to represent interactions between these elements in the form of complex network. After this step, the study of complex system organization is reduced to the analysis of structure and dynamical processes on network with the use of suitable methodology. The increase in a variety of real systems with available data, which enable insight into the structure of network of interactions, requires constant development of new techniques and theoretical models that could explain behavior of specific systems. In this thesis, we studied complex networks with discrete dynamics using data on event-based social systems. There has been very little previous research on properties of networks representing these systems. One of the main reasons is availability of data. In the given systems individuals interact face-to-face, wherefore it is more difficult to get the data, than in the case of social systems where individuals use some communication device to communicate with each other. Special attention was paid to examination of activity of individuals in group events. According to the results of statistical analysis of empirical data it has been shown that individuals do not attend events randomly. We analysed mathematical models that can explain member’s participation patterns on events which turned out to be strongly heterogeneous. It has been shown that generalized binary P´olya model can reproduce given empirical results successfully. Using bipartite networks ensemble with maximum entropy, we identified significant connections in weighted network that represent relevant social interactions. In order to get the insight into evolution of the network structure, we analyzed change of local structural parameters after each event attendance. It has been shown that members of the system establish new connections with neighbors during member’s early involvement in the group activities, while later, as number of attended events increase, the interactions with neighbors and strenghtening of existing communities become preferred in comparison to forming new connections in network. In order to analyse the influence that particular event has on network structure, we proposed an approach based on event removal according to different criteria and examination of resulting structural changes in network. The results showed that interactions between individuals with strong connections are dominant on events with small number of members, with small number of members, while during the large events typically individuals with weak connections that could be easily broken interact.