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http://hdl.handle.net/2445/203675
Title: | Estimating the dimensionality of complex networks using persistent homology |
Author: | Vila Miñana, Meritxell |
Director/Tutor: | Casacuberta, Carles Ferrà Marcús, Aina |
Keywords: | Homologia Topologia algebraica Teoria de grafs Treballs de fi de grau Homology Algebraic topology Graph theory Bachelor's theses |
Issue Date: | 13-Jun-2023 |
Abstract: | [en] In this work, a new interdisciplinary approach is presented to study the dimensionality of complex networks using techniques from topological data analysis (TDA) through a filtration of graphs by vertex degrees. For each of two real-world complex networks, 30 surrogate graphs were generated in each dimension from 1 to 10, and several TDA descriptors of graphs were compared with the corresponding values for the real networks in order to estimate their latent dimension. Total persistence, Wasserstein distance and scale-space kernel dissimilarity, among other descriptors, yielded consistent outcomes. The results of this study suggest that TDA is sensible to the latent dimension of complex networks, and provide conclusions consistent with those obtained in previous studies. |
Note: | Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2023, Director: Carles Casacuberta |
URI: | http://hdl.handle.net/2445/203675 |
Appears in Collections: | Treballs Finals de Grau (TFG) - Matemàtiques |
Files in This Item:
File | Description | Size | Format | |
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tfg_meritxell_vila_miñana.pdf | Memòria | 6.1 MB | Adobe PDF | View/Open |
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