Dresden 2009 – wissenschaftliches Programm
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AGSOE: Arbeitsgruppe Physik sozio-ökonomischer Systeme
AGSOE 19: Networks: From Topology to Dynamics IV
AGSOE 19.1: Vortrag
Donnerstag, 26. März 2009, 16:00–16:30, BAR 205
Statistical Mechanics and Homology of Neighborhod Complexes — •Danijela Horak1, Slobodan Maletic2, and Milan Rajkovic2 — 1Max Planck Institute for Mathematics in the Natural Sciences, Leipzig — 2Institute of Nuclear Sciences Vinca, Belgrade
Complex networks are encoded into simplicial complexes (neighborhood complexes) and analyzed from alegbraic, combinatorial and topological aspect. Certian topological invariants are shown to have distinct statistical properties and in analogy to statistical mechanics of networks we develop a statistical mechanics of simplicial complexes. Long lived topological features, considered as topological signal, are distinguished from short lived ones, considered as topological noise. A new topological invariant, persistent homology, is determined and presented as a parametrized version of a Betti number. Complex networks with distinct degree distributions exhibit distinct persistent topological features. Persistent toplogical attributes, shown to be related to robust quality of networks, also reflect defficiency in certain connectivity properites of networks. Random networks, networks with exponential conectivity distribution and scale-free networks are considered for homological persistency analysis. Furthermore, the advantages of such an approach and new results are illustrated in applications to economic and social models on networks (e.g. Axelrod model and its variants).