TY - JOUR
T1 - Simplicial complexes and complex systems
AU - Salnikov, Vsevolod
AU - Cassese, Daniele
AU - Lambiotte, Renaud
PY - 2019/1/1
Y1 - 2019/1/1
N2 - We provide a short introduction to the field of topological data analysis (TDA) and discuss its possible relevance for the study of complex systems. TDA 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 the 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.
AB - We provide a short introduction to the field of topological data analysis (TDA) and discuss its possible relevance for the study of complex systems. TDA 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 the 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.
KW - network science
KW - persistence homology
KW - simplicial complexes
KW - topological data analysis
UR - http://www.scopus.com/inward/record.url?scp=85057193741&partnerID=8YFLogxK
U2 - 10.1088/1361-6404/aae790
DO - 10.1088/1361-6404/aae790
M3 - Article
AN - SCOPUS:85057193741
SN - 0143-0807
VL - 40
JO - European Journal of Physics
JF - European Journal of Physics
IS - 1
M1 - 014001
ER -