Organization of information pathways in complex networks

University dissertation from Umea?, Sweden : Umeå University

Abstract: A shuman beings, we are continuously struggling to comprehend the mechanism of dierent natural systems. Many times, we face a complex system where the emergent properties of the system at a global level can not be explained by a simple aggregation of the system's components at the micro-level. To better understand the macroscopic system eects, we try to model microscopic events and their interactions. In order to do so, we rely on specialized tools to connect local mechanisms with global phenomena. One such tool is network theory. Networks provide a powerful way of modeling and analyzing complex systems based on interacting elements. The interaction pattern links the elements of the system together and provides a structure that controls how information permeates throughout the system. For example, the passing of information about job opportunities in a society depends on how social ties are organized. The interaction pattern, therefore, often is essential for reconstructing and understanding the global-scale properties of the system.In this thesis, I describe tools and models of network theory that we use and develop to analyze the organization of social or transportation systems. More specifically, we explore complex networks by asking two general questions: First, which mechanistic theoretical models can better explain network formation or spreading processes on networks? And second, what are the signi cant functional units of real networks? For modeling, for example, we introduce a simple agent-based model that considers interacting agents in dynamic networks that in the quest for information generate groups. With the model, we found that the network and the agents' perception are interchangeable; the global network structure and the local information pathways are so entangled that one can be recovered from the other one. For investigating signi cant functional units of a system, we detect, model, and analyze signi cant communities of the network. Previously introduced methods of significance analysis suer from oversimpli ed sampling schemes. We have remedied their shortcomings by proposing two dierent approaches: rst by introducing link prediction and second by using more data when they are available. With link prediction, we can detect statistically signi cant communities in large sparse networks. We test this method on real networks, the sparse network of the European Court of Justice case law, for example, to detect signi cant and insigni cant areas of law. In the presence of large data, on the other hand, we can investigate how underlying assumptions of each method aect the results of the signi cance analysis. We used this approach to investigate dierent methods for detecting signi cant communities of time-evolving networks. We found that, when we highlight and summarize important structural changes in a network, the methods that maintain more dependencies in signi cance analysis can predict structural changes earlier.In summary, we have tried to model the systems with as simple rules as possible to better understand the global properties of the system. We always found that maintaing information about the network structure is essential for explaining important phenomena on the global scale. We conclude that the interaction pattern between interconnected units, the network, is crucial for understanding the global behavior of complex systems because it keeps the system integrated. And remember, everything is connected, albeit not always directly.