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Ŀ¼ 1 Introduction
1.1 Complex system
1.2 Complex networks
1.3 Simplicial Complexes
Bibliography
2 The World of Simplicial Complexes
2.1 Geometric simplicial complex
2.2 Abstract simplicial complex
2.3 Simplicial complex via relation
2.4 Characterization of simplicial complexes
2.5 Summary
Bibliography
3 How Do We Build Simplicial Complexes
3.1 From complex networks £¨graphs£©
3.2 From data in metric space
3.3 From time series
3.4 Summary
Bibliography
4 SeveraIApplications of Simplicial Complexes
4.1 Opinion exchange modeling
4.2 Topological description of the air traffic control network
4.3 Topological properties of dynamical systems
4.4 Instead of summary£º Potential contributions to aeronautical science
Bibliography
5 Take—home Messages
5.1 Briefbook summary
5.2 Suggestions for further reading