Simplicial complexes and complex systems

Understand

We provide a short introduction to the field of topological data analysis and discuss its possible relevance for the study of complex systems.

• Topological data analysis provides a set of tools to characterise the shape of data, in terms of the presence of holes or cavities between the points.
• The methods, based on notion of simplicial complexes, generalise standard network tools by naturally allowing for many-body interactions and providing results robust under continuous deformations of the data.
• We present strengths and weaknesses of current methods, as well as a range of empirical studies relevant to the field of complex systems, before identifying future methodological challenges to help understand the emergence of collective phenomena.