Simplicial complexes of networks and their statistical properties
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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 numbers
Source:Lecture Notes in Computer Science / Lecture Notes in Artificial Intelligence, 2008, 5102, 568-575
- 8th International Conference on Computational Science, Jun 23-25, 2008, Cracow, Poland