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Higher-order networks describe the many-body interactions of a large variety of complex systems, ranging from the the brain to collaboration networks. Simplicial complexes are generalized network structures which allow us to capture the combinatorial properties, the topology and the geometry of higher-order networks. Having been used extensively in quantum gravity to describe discrete or discretized space-time, simplicial complexes have only recently started becoming the representation of choice for capturing the underlying network topology and geometry of complex systems. This Element provides an in-depth introduction to the very hot topic of network theory, covering a wide range of subjects ranging from emergent hyperbolic geometry and topological data analysis to higher-order dynamics. This Elements aims to demonstrate that simplicial complexes provide a very general mathematical framework to reveal how higher-order dynamics depends on simplicial network topology and geometry.
Biological systems are extremely complex and have emergent properties that cannot be explained or even predicted by studying their individual parts in isolation. The reductionist approach, although successful in the early days of molecular biology, underestimates this complexity. As the amount of available data grows, so it will become increasingly important to be able to analyse and integrate these large data sets. This book introduces novel approaches and solutions to the Big Data problem in biomedicine, and presents new techniques in the field of graph theory for handling and processing multi-type large data sets. By discussing cutting-edge problems and techniques, researchers from a wide range of fields will be able to gain insights for exploiting big heterogonous data in the life sciences through the concept of 'network of networks'.