2026-04-17T11:47:31Zhttps://recercat.cat/oai/request

oai:recercat.cat:2099.1/131192025-07-23T03:24:57Zcom_2072_1033col_2072_452951

00925njm 22002777a 4500 dc Colomer de Simón, Pol author 2011-09-22 Projecte final de Màster Oficial reaizat en col.laboració amb Universitat de Barcelona. Departament de Física Fonamental. 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. Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica Anàlisi de conglomerats Hyperbolic spaces Complex Hyperbolic Clustering Network Cluster analysis Espais hiperbòlics Characterization of the clustering phase transition of a complex network embedded in a hyperbolic plane