Heterogeneous Networks on Multiple Levels

At any moment in time, we are driven by and are an integral part of many interconnected, dynamically changing networks. Our species has evolved as part of diverse ecological, biological, social, and other networks over thousands of years. As part of a complex food web, we learned how to find prey and to avoid predators. We have created advanced socio-technical environments in the shape of cities, water and power networks, streets, and airline systems. In 1969, people started to interlink computers leading to the largest and most widely used networked communication infrastructure in existence today: the Internet. Often, the complex structure of networks is influenced by system-dependent local constraints on the node interconnectivity. Node characteristics may vary over time and there might be many di↵erent types of nodes. The links1 between nodes might be directed or undirected, and might have weights and/or additional properties that might change over time. Many natural systems never reach a steady state and non-equilibrium models need to be applied to characterize their behavior. As a result of this usually domain-specific complexity, analysts are not only confronted with large multivariate networks. In practice, those networks can be assigned to di↵erent levels (or scales), and it is absolutely possible that several di↵erent networks share the same level. In case a set of networks share the same level, several notions of those networks can be found in the literature: they reach from multimodal networks, network of networks to heterogeneous networks. For simplicity, we use the latter term for the remainder of this chapter. Complex structures of heterogeneous networks distributed over various levels lead to considerable visualization and analysis problems. First, the possibly tremendous size and complexity (in terms of higher dimensionality of the node/edge attributes) of those networks form a challenge of itself that is also discussed by other chapters of this book. Second and more impor-