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We live in a tightly knit world. Our emotions, desires, perceptions and decisions are interlinked in our interactions with others. We are constantly influencing our surroundings and being influenced by others. In this thesis, we unfold some aspects of social and economical interactions by studying empirical datasets. We project these interactions into a network representation to gain insights on how socio-economic systems form and function and how they change over time. Specifically, this thesis is centered on four main questions: How do the means of communication shape our social network structures? How can we uncover the underlying network of interests from massive observational data? How does a crisis spread in a real financial network? How do the dynamics of interaction influence spreading processes in networks? We use a variety of methods from physics, psychology, sociology, and economics as well as computational, mathematical and statistical analysis to address these questions.

Complex systems play an essential role in our daily lives. These systems consist of many connected components that interact with each other. Consider, for example, society with billions of collaborating individuals, the stock market with numerous buyers and sellers that trade equities, or communication infrastructures with billions of phones, computers and satellites.

The key to understanding complex systems is to understand the interaction patterns between their components - their networks. To create the network, we need data from the system and a model that organizes the given data in a network representation. Today's increasing availability of data and improved computational capacity for analyzing networks have created great opportunities for the network approach to further prosper. However, increasingly rich data also gives rise to new challenges that question the effectiveness of the conventional approach to modeling data as a network. In this thesis, we explore those challenges and provide methods for simplifying and highlighting important interaction patterns in network models that make use of richer data.

Using data from real-world complex systems, we first show that conventional network modeling can provide valuable insights about the function of the underlying system. To explore the impact of using richer data in the network representation, we then expand the analysis for higher-order models of networks and show why we need to go beyond conventional models when there is data that allows us to do so. In addition, we also present a new framework for higher-order network modeling and analysis. We find that network models that capture richer data can provide more accurate representations of many real-world complex systems.