Simplicial complexes of networks and their statistical properties
Abstract
Topological, algebraic and combinatorial properties of simplicial complexes which are constructed from networks (graphs) are examined from the statistical point of view. We show that basic statistical features of scale free networks are preserved by topological invariants of simplicial complexes and similarly statistical properties pertaining to topological invariants of other types of networks are preserved as well. Implications and advantages of such an approach to various research areas involving network concepts are discussed.
Keywords:
networks / statistical mechanics / complex systems / topology / simplicial complexes / homology / betti numbersSource:
Lecture Notes in Computer Science / Lecture Notes in Artificial Intelligence, 2008, 5102, 568-575Note:
- 8th International Conference on Computational Science, Jun 23-25, 2008, Cracow, Poland
Collections
Institution/Community
VinčaTY - CONF AU - Maletić, Slobodan AU - Rajković, Milan AU - Vasiljević, Danijela PY - 2008 UR - https://vinar.vin.bg.ac.rs/handle/123456789/6764 AB - Topological, algebraic and combinatorial properties of simplicial complexes which are constructed from networks (graphs) are examined from the statistical point of view. We show that basic statistical features of scale free networks are preserved by topological invariants of simplicial complexes and similarly statistical properties pertaining to topological invariants of other types of networks are preserved as well. Implications and advantages of such an approach to various research areas involving network concepts are discussed. C3 - Lecture Notes in Computer Science / Lecture Notes in Artificial Intelligence T1 - Simplicial complexes of networks and their statistical properties VL - 5102 SP - 568 EP - 575 UR - https://hdl.handle.net/21.15107/rcub_vinar_6764 ER -
@conference{ author = "Maletić, Slobodan and Rajković, Milan and Vasiljević, Danijela", year = "2008", abstract = "Topological, algebraic and combinatorial properties of simplicial complexes which are constructed from networks (graphs) are examined from the statistical point of view. We show that basic statistical features of scale free networks are preserved by topological invariants of simplicial complexes and similarly statistical properties pertaining to topological invariants of other types of networks are preserved as well. Implications and advantages of such an approach to various research areas involving network concepts are discussed.", journal = "Lecture Notes in Computer Science / Lecture Notes in Artificial Intelligence", title = "Simplicial complexes of networks and their statistical properties", volume = "5102", pages = "568-575", url = "https://hdl.handle.net/21.15107/rcub_vinar_6764" }
Maletić, S., Rajković, M.,& Vasiljević, D.. (2008). Simplicial complexes of networks and their statistical properties. in Lecture Notes in Computer Science / Lecture Notes in Artificial Intelligence, 5102, 568-575. https://hdl.handle.net/21.15107/rcub_vinar_6764
Maletić S, Rajković M, Vasiljević D. Simplicial complexes of networks and their statistical properties. in Lecture Notes in Computer Science / Lecture Notes in Artificial Intelligence. 2008;5102:568-575. https://hdl.handle.net/21.15107/rcub_vinar_6764 .
Maletić, Slobodan, Rajković, Milan, Vasiljević, Danijela, "Simplicial complexes of networks and their statistical properties" in Lecture Notes in Computer Science / Lecture Notes in Artificial Intelligence, 5102 (2008):568-575, https://hdl.handle.net/21.15107/rcub_vinar_6764 .