# Regensburg 2013 – wissenschaftliches Programm

## Bereiche | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe

# DY: Fachverband Dynamik und Statistische Physik

## DY 7: Poster I

### DY 7.14: Poster

### Montag, 11. März 2013, 17:30–19:30, Poster C

**Hierarchy in directed networks** — •Krzysztof Suchecki and Janusz Hołyst — Faculty of Physics, Center of Excellence for Complex Systems Research, Warsaw University of Technology, ul. Koszykowa 75, Warszawa, Poland

We introduce a definition of observable hierarchy in directed networks, related to the possible information or command flows in such networks and derived purely from the network topology. For trees, it is a simple average distance of leaf vertices from the root plus one. We generalize it for any directed network. In case of presence of directed loops, we assign all the vertices in a loop to the same hierarchy, which effectively means treating loops as single complex vertices. We analyze the average hierarchy value for different types of networks and in case of network models investigate its dependence on network parameters, as well as explain the obtained results. For directed Erdos-Renyi random graphs, we observe maximum hierarchy value depending on the graph density, that coincides with the percolation threshold.