# Regensburg 2013 – wissenschaftliches Programm

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# DY: Fachverband Dynamik und Statistische Physik

## DY 11: Statistics and Dynamics of/on Networks (joint session BP/DY/SOE)

### DY 11.4: Vortrag

### Dienstag, 12. März 2013, 10:15–10:30, H47

**Robust large-scale properties in networks** — •Tiago Peixoto and Stefan Bornholdt — Institut für Theoretische Physik, Universität Bremen, Hochschulring 18, D-28359 Bremen, Germany

Most network systems possess large- or mesoscale structures, which are not captured by local measures such as, e.g. degree and subgraph statistics. Many network models, as well as mean field analysis of dynamical processes on networks neglect such features. Here we include in a general fashion such large-scale properties in the the analysis of a paradigmatic percolation problem in networks with interdependence, as well as Boolean dynamics based on majority functions, meant to describe systems which are robust against noise, such as gene regulation.

A model for the evolution of such systems is proposed, where networks with more robust properties survive with greater probability. By mapping the evolutionary process into a statistical ensemble, the free energy of the system is minimized, and its equilibrium properties are obtained. The analysis reveals a topological phase transition at a specific value of selective pressure, where a core-periphery topology emerges, characterized by the existence of a smaller subset of nodes which regulate the entire system; a feature which is also found in many real systems.

T. P. Peixoto, S. Bornholdt, Phys. Rev. Lett. 109, 118703 (2012); T. P. Peixoto, Phys. Rev. E 85, 041908 (2012); T. P. Peixoto, Phys. Rev. E 85, 056122 (2012)