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## Procesy transportu i ewolucja topologii hierarchicznych sieci złożonych

### Agnieszka Czaplicka

#### Abstract

The thesis focuses on models of hierarchical networks. Emergence scenarios and transport efficiency in the presence of noise in such systems are considered. ”Top - down” models (from the best level to the worst) are based on individuals’ tendency to situate themselves in hierarchy close to the node (root) which initiated network creation. We assumed that newcomers know positions of given set of nodes and choose the one which is the closest to the root node (tournament where the best wins). Two types of tournament are proposed: with a constant number of participants, independent of network size (model C), and where the number of participants is proportional to the system size (model P). Tournament size is related to information about network available to each new node. In the model C all hierarchies can emerge (if evolution runs long enough). In the model P the first level (next to the root) always emerges but worse levels either do not emerge at all or they appear only by chance in the early stage of system evolution to further stop growing at all. In the case of ”bottom - up” model the dynamics consists of processes corresponding to nodes promotions and degradations to the system ground state. After the phase of growth of hierarchies, the system reaches stationary state. Average hierarchy level, number of edges per node and fraction of nodes at ground level do not depend on system size. Distribution of nodes at hierarchy level is exponential. Critical value of the ratio of number degradations and promotions above which hierarchies do not emerge is close to systemsize. The influence of noise on transport efficiency in static hierarchical networks was examined. We considered topological noise (change of network topology in comparison to original one) and dynamical noise (agents perform random walk instead of following the usual dynamical rules). Different kinds of hierarchical topologies were considered. We observed that negative influence of one type of noise can be eliminated by the presence of other one. We noticed optimal efficiency of packet transfer for non-zero values of both stochastic components. Results for artificial networks were compared with efficiency of real network. The thesis is based on four publications [1]-[4].
Record ID
WUTd314e8baf59c4c9c92b6c65c68490b39
Diploma type
Doctor of Philosophy
Author
Agnieszka Czaplicka Agnieszka Czaplicka,, Center of Physics in Economics and Social Sciences (FP/LPESS)Faculty of Physics (FP)
Title in Polish
Procesy transportu i ewolucja topologii hierarchicznych sieci złożonych
Language
(pl) Polish
Certifying Unit
Faculty of Physics (FP)
Discipline
physics / (physical sciences domain) / (physical sciences)
Status
Finished
Start date
01-10-2010
Defense Date
20-10-2014
Title date
20-10-2014
Supervisor
External reviewers
Krzysztof Kułakowski Krzysztof Kułakowski,, External affiliation of publication: AGH University of Science and Technology
Katarzyna Sznajd-Weron Katarzyna Sznajd-Weron,, External affiliation of publication: Wroclaw University of Science and Technology
Pages
107
Keywords in English
hierarchical networks, transport processes, topology evolution
Abstract in English
The thesis focuses on models of hierarchical networks. Emergence scenarios and transport efficiency in the presence of noise in such systems are considered. ”Top - down” models (from the best level to the worst) are based on individuals’ tendency to situate themselves in hierarchy close to the node (root) which initiated network creation. We assumed that newcomers know positions of given set of nodes and choose the one which is the closest to the root node (tournament where the best wins). Two types of tournament are proposed: with a constant number of participants, independent of network size (model C), and where the number of participants is proportional to the system size (model P). Tournament size is related to information about network available to each new node. In the model C all hierarchies can emerge (if evolution runs long enough). In the model P the first level (next to the root) always emerges but worse levels either do not emerge at all or they appear only by chance in the early stage of system evolution to further stop growing at all. In the case of ”bottom - up” model the dynamics consists of processes corresponding to nodes promotions and degradations to the system ground state. After the phase of growth of hierarchies, the system reaches stationary state. Average hierarchy level, number of edges per node and fraction of nodes at ground level do not depend on system size. Distribution of nodes at hierarchy level is exponential. Critical value of the ratio of number degradations and promotions above which hierarchies do not emerge is close to systemsize. The influence of noise on transport efficiency in static hierarchical networks was examined. We considered topological noise (change of network topology in comparison to original one) and dynamical noise (agents perform random walk instead of following the usual dynamical rules). Different kinds of hierarchical topologies were considered. We observed that negative influence of one type of noise can be eliminated by the presence of other one. We noticed optimal efficiency of packet transfer for non-zero values of both stochastic components. Results for artificial networks were compared with efficiency of real network. The thesis is based on four publications [1]-[4].
Project (archive)
Thesis file
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Citation count
2

Uniform Resource Identifier
https://repo.pw.edu.pl/info/phd/WUTd314e8baf59c4c9c92b6c65c68490b39/
URN
urn:pw-repo:WUTd314e8baf59c4c9c92b6c65c68490b39

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