Berlin 2015 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 59: Poster - networks

DY 59.5: Poster

Donnerstag, 19. März 2015, 16:00–18:00, Poster A

Symmetry-based coarse-graining of regular evolved networks — •Steffen Karalus and Joachim Krug — Institut für Theoretische Physik, Universität zu Köln

Virtually all empirical network structures are adjusted to their functional requirements by some evolutionary process adapting the topology for the specific needs. In most cases the functionality of a network is associated with the global behavior of dynamical processes based on the network. Many important processes are governed by the graph Laplacian. Its spectrum determines the overall behavior of such dynamics on a network. The strategy of evolutionary optimization can be successfully applied to find networks with a specific spectral dimension (power-law in the Laplacian spectrum) such that a non-trivial (subdiffusive) dynamical behavior emerges [1].

Networks evolved under the additional constraint of k-regularity exhibit an abundance of certain symmetric motifs. This can be exploited to construct quotient networks as systematic coarse-graining based on network symmetry [2]. This coarse-graining removes redundancies but retains the overall network structure. In this way we obtain a significant simplification of the evolved networks while the power-law spectrum and spectral dimension are preserved.

[1] S. Karalus and M. Porto, EPL 99, 38002 (2012).

[2] B. D. MacArthur and R. J. Sánchez-García, Phys. Rev. E 80, 026117 (2009).