Networks are an important tool for analyzing and visualizing different complex systems. Examples of real-world networks include social network of friends on Facebook, technological network of railways, biological network of interactions between proteins and information networks of hyperlinks between the Web pages. The evolution of the Web and the capability of storing large amounts of data have caused the size of networked systems and their complexity to increase. However, the algorithms for network analysis and visualization appear impractical for addressing very large systems. Furthermore, data about networks are not always complete, their structure may be hidden, or they may change quickly over time. Any network studied in the literature is thus inevitably just a simplified representative of its real-world analogue. For these reasons, understanding how an incomplete system differs from a complete one is crucial. Recently, a number of techniques have been proposed for simplifying complex networks. The simplification is a process, which reduce the size of a large network with merging, sampling or exploration of nodes or links in a network. Simplification techniques are applied to large networks to allow for their faster and more efficient analysis. Since the findings of the analyses and simulations of simplified networks are implied for the original ones, it is of key importance to understand the structural differences between the original networks and their simplified variants.
Network simplification has been extensively investigated from different perspectives. A large number of studies focus on the changes in network properties introduced by simplification. On the other hand, only a few studies compare simplification techniques. In this doctoral thesis, we study the changes of real-world networks introduced by simplification and analyze the differences among simplification techniques. We propose an approach for assessing the effectiveness of simplification. Based on the similarity between original and simplified networks, we compare different simplification techniques. We simplify a number of real-world networks of various types and sizes and explore the preservation of network properties on simplified networks of different sizes. We analyze the changes of network density under the simplification and compare characteristic groups of nodes in original and simplified networks. Based on the findings of the analyses we introduce the scheme for choosing the appropriate simplification technique for a particular network.
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