Characterization of the clustering phase transition of a complex network embedded in a hyperbolic plane
Visualitza/Obre
Estadístiques de LA Referencia / Recolecta
Inclou dades d'ús des de 2022
Cita com:
hdl:2099.1/13119
Tutor / directorBoguñá Espinal, Marian
Tipus de documentProjecte Final de Màster Oficial
Data2011-09-22
Condicions d'accésAccés obert
Llevat que s'hi indiqui el contrari, els
continguts d'aquesta obra estan subjectes a la llicència de Creative Commons
:
Reconeixement-NoComercial-SenseObraDerivada 3.0 Espanya
Abstract
English: If we distribute nodes homogeneously in an hyperbolic plane and connect each possible pair of nodes with a probability that depends on the hyperbolic distance among them, heterogeneous degree distributions and strong clustering emerge naturally. Both metrics are key properties observed in real complex networks but are rarely seen together in standard network models. Our model considers edges in a network as noninteracting fermions whose energies are equal to the hyperbolic distances between nodes. This interpretation allows us to use statistical mechanics methods, like the Metropolis Hastings algorithm, in order to perform numerical simulations and to get precise measurements of the network properties. In this master thesis, we focus on the study of clustering, which undergoes a phase transition at a certain critical temperature. We develop an analytical framework to obtain the critical exponents of this phase transition and compare them with numerical simulations. Finally, we check whether the Finite Size Scaling (FSS) assumption holds in this case or not.
Descripció
Projecte final de Màster Oficial reaizat en col.laboració amb Universitat de Barcelona. Departament de Física Fonamental.
TitulacióMÀSTER UNIVERSITARI EN FÍSICA COMPUTACIONAL I APLICADA (Pla 2009)
Fitxers | Descripció | Mida | Format | Visualitza |
---|---|---|---|---|
TFM_Pol Colomer.pdf | 379,0Kb | Visualitza/Obre |